Displaying similar documents to “The representation of multi-hypergraphs by set intersections”

Composition in ultradifferentiable classes

Armin Rainer, Gerhard Schindl (2014)

Studia Mathematica

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We characterize stability under composition of ultradifferentiable classes defined by weight sequences M, by weight functions ω, and, more generally, by weight matrices , and investigate continuity of composition (g,f) ↦ f ∘ g. In addition, we represent the Beurling space ( ω ) and the Roumieu space ω as intersection and union of spaces ( M ) and M for associated weight sequences, respectively.

Solutions to the equation div u = f in weighted Sobolev spaces

Katrin Schumacher (2008)

Banach Center Publications

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We consider the problem div u = f in a bounded Lipschitz domain Ω, where f with Ω f = 0 is given. It is shown that the solution u, constructed as in Bogovski’s approach in [1], fulfills estimates in the weighted Sobolev spaces W w k , q ( Ω ) , where the weight function w is in the class of Muckenhoupt weights A q .

Weighted Frobenius-Perron operators and their spectra

Mohammad Reza Jabbarzadeh, Rana Hajipouri (2017)

Mathematica Bohemica

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First, some classic properties of a weighted Frobenius-Perron operator 𝒫 ϕ u on L 1 ( Σ ) as a predual of weighted Koopman operator W = u U ϕ on L ( Σ ) will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of 𝒫 ϕ u under certain conditions.

Existence and regularity of solutions of some elliptic system in domains with edges

Wojciech M. Zajączkowski

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CONTENTS1. Introduction.......................................................................52. Notation and auxiliary results............................................93. Statement of the problem (1.1)-(1.3)..............................204. The problem (3.14).........................................................225. Auxiliary results in D ϑ ...............................................346. Existence of solutions of (3.14) in H μ k ( D ϑ ) ............417. Green function................................................................528....

Polyanalytic Besov spaces and approximation by dilatations

Ali Abkar (2024)

Czechoslovak Mathematical Journal

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Using partial derivatives f / z and f / z ¯ , we introduce Besov spaces of polyanalytic functions in the open unit disk, as well as in the upper half-plane. We then prove that the dilatations of functions in certain weighted polyanalytic Besov spaces converge to the same functions in norm. When restricted to the open unit disk, we prove that each polyanalytic function of degree q can be approximated in norm by polyanalytic polynomials of degree at most q .

Remarks on the critical Besov space and its embedding into weighted Besov-Orlicz spaces

Hidemitsu Wadade (2010)

Studia Mathematica

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We present several continuous embeddings of the critical Besov space B p n / p , ρ ( ) . We first establish a Gagliardo-Nirenberg type estimate | | u | | q , w r 0 , ν C ( 1 / ( n - r ) ) 1 / q + 1 / ν - 1 / ρ ( q / r ) 1 / ν - 1 / ρ | | u | | p 0 , ρ ( n - r ) p / n q | | u | | p n / p , ρ 1 - ( n - r ) p / n q , for 1 < p ≤ q < ∞, 1 ≤ ν < ρ ≤ ∞ and the weight function w r ( x ) = 1 / ( | x | r ) with 0 < r < n. Next, we prove the corresponding Trudinger type estimate, and obtain it in terms of the embedding B p n / p , ρ ( ) B Φ , w r 0 , ν ( ) , where the function Φ₀ of the weighted Besov-Orlicz space B Φ , w r 0 , ν ( ) is a Young function of the exponential type. Another point of interest is to embed B p n / p , ρ ( ) into the weighted Besov...

Lipschitz continuity in Muckenhoupt 𝓐₁ weighted function spaces

Dorothee D. Haroske (2011)

Banach Center Publications

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We study continuity envelopes of function spaces B p , q s ( , w ) and F p , q s ( , w ) where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.

Some weighted norm inequalities for a one-sided version of g * λ

L. de Rosa, C. Segovia (2006)

Studia Mathematica

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We study the boundedness of the one-sided operator g λ , φ between the weighted spaces L p ( M ¯ w ) and L p ( w ) for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of g λ , φ . For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of g λ , φ from L p ( ( M ¯ ) [ p / 2 ] + 1 w ) to L p ( w ) , where ( M ¯ ) k denotes the operator M¯ iterated k times.

Existence of solutions to the (rot,div)-system in L p -weighted spaces

Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, v · n ̅ | S = 0 , S = ∂Ω in weighted L p -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.

New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces

Xin-Cui Guo, Ze-Hua Zhou (2015)

Czechoslovak Mathematical Journal

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Let u be a holomorphic function and ϕ a holomorphic self-map of the open unit disk 𝔻 in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators u C ϕ from Zygmund type spaces to Bloch type spaces in 𝔻 in terms of u , ϕ , their derivatives, and ϕ n , the n -th power of ϕ . Moreover, we obtain some similar estimates for the essential norms of the operators u C ϕ , from which sufficient and necessary conditions of compactness of u C ϕ follows immediately. ...

Weighted sub-Bergman Hilbert spaces

Maria Nowak, Renata Rososzczuk (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces A α 2 , 1 < α < . These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers.

Weighted H p spaces

José García-Cuerva

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CONTENTSIntroduction.......................................................................................................................................................... 5Chapter I. Some preliminary lemmas............................................................................................................ 8Chapter II. Weighted H p spaces of analytic functions.......................................................................... 13 1. Behaviour at the boundary..........................................................................................................................

Lacunary series in Q K spaces

Hasi Wulan, Kehe Zhu (2007)

Studia Mathematica

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Under mild conditions on the weight function K we characterize lacunary series in the so-called K spaces.

Order convexity and concavity of Lorentz spaces Λ p , w , 0 < p < ∞

Anna Kamińska, Lech Maligranda (2004)

Studia Mathematica

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We study order convexity and concavity of quasi-Banach Lorentz spaces Λ p , w , where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that Λ p , w contains an order isomorphic copy of l p . We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for Λ p , w . We conclude with a characterization of the type and cotype of Λ p , w in the case when Λ p , w is a normable space.

Rademacher functions in Cesàro type spaces

Sergei V. Astashkin, Lech Maligranda (2010)

Studia Mathematica

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The Rademacher sums are investigated in the Cesàro spaces C e s p (1 ≤ p ≤ ∞) and in the weighted Korenblyum-Kreĭn-Levin spaces K p , w on [0,1]. They span l₂ space in C e s p for any 1 ≤ p < ∞ and in K p , w if and only if the weight w is larger than t l o g p / 2 ( 2 / t ) on (0,1). Moreover, the span of the Rademachers is not complemented in C e s p for any 1 ≤ p < ∞ or in K 1 , w for any quasi-concave weight w. In the case when p > 1 and when w is such that the span of the Rademacher functions is isomorphic to l₂, this span is...

Spectral radius of weighted composition operators in L p -spaces

Krzysztof Zajkowski (2010)

Studia Mathematica

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We prove that for the spectral radius of a weighted composition operator a T α , acting in the space L p ( X , , μ ) , the following variational principle holds: l n r ( a T α ) = m a x ν M ¹ α , e X l n | a | d ν , where X is a Hausdorff compact space, α: X → X is a continuous mapping preserving a Borel measure μ with suppμ = X, M ¹ α , e is the set of all α-invariant ergodic probability measures on X, and a: X → ℝ is a continuous and -measurable function, where = n = 0 α - n ( ) . This considerably extends the range of validity of the above formula, which was previously known...

A weighted inequality for the Hardy operator involving suprema

Pavla Hofmanová (2016)

Commentationes Mathematicae Universitatis Carolinae

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Let u be a weight on ( 0 , ) . Assume that u is continuous on ( 0 , ) . Let the operator S u be given at measurable non-negative function ϕ on ( 0 , ) by S u ϕ ( t ) = sup 0 < τ t u ( τ ) ϕ ( τ ) . We characterize weights v , w on ( 0 , ) for which there exists a positive constant C such that the inequality 0 [ S u ϕ ( t ) ] q w ( t ) d t 1 q 0 [ ϕ ( t ) ] p v ( t ) d t 1 p holds for every 0 < p , q < . Such inequalities have been used in the study of optimal Sobolev embeddings and boundedness of certain operators on classical Lorenz spaces.

Weighted integrability of double cosine series with nonnegative coefficients

Chang-Pao Chen, Ming-Chuan Chen (2003)

Studia Mathematica

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Let f c ( x , y ) j = 1 k = 1 a j k ( 1 - c o s j x ) ( 1 - c o s k y ) with a j k 0 for all j,k ≥ 1. We estimate the integral 0 π 0 π x α - 1 y β - 1 ϕ ( f c ( x , y ) ) d x d y in terms of the coefficients a j k , where α, β ∈ ℝ and ϕ: [0,∞] → [0,∞]. Our results can be regarded as the trigonometric analogues of those of Mazhar and Móricz [MM]. They generalize and extend Boas [B, Theorem 6.7].

Isometric composition operators on weighted Dirichlet space

Shi-An Han, Ze-Hua Zhou (2016)

Czechoslovak Mathematical Journal

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We investigate isometric composition operators on the weighted Dirichlet space 𝒟 α with standard weights ( 1 - | z | 2 ) α , α > - 1 . The main technique used comes from Martín and Vukotić who completely characterized the isometric composition operators on the classical Dirichlet space 𝒟 . We solve some of these but not in general. We also investigate the situation when 𝒟 α is equipped with another equivalent norm.

Beurling algebra analogues of theorems of Wiener-Lévy-Żelazko and Żelazko

S. J. Bhatt, P. A. Dabhi, H. V. Dedania (2009)

Studia Mathematica

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Let 0 < p ≤ 1, let ω: ℤ → [1,∞) be a weight on ℤ and let f be a nowhere vanishing continuous function on the unit circle Γ whose Fourier series satisfies n | f ̂ ( n ) | p ω ( n ) < . Then there exists a weight ν on ℤ such that n | ( 1 / f ) ^ ( n ) | p ν ( n ) < . Further, ν is non-constant if and only if ω is non-constant; and ν = ω if ω is non-quasianalytic. This includes the classical Wiener theorem (p = 1, ω = 1), Domar theorem (p = 1, ω is non-quasianalytic), Żelazko theorem (ω = 1) and a recent result of Bhatt and Dedania (p = 1). An...

Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces

George Kyriazis, Pencho Petrushev, Yuan Xu (2008)

Studia Mathematica

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The Littlewood-Paley theory is extended to weighted spaces of distributions on [-1,1] with Jacobi weights w ( t ) = ( 1 - t ) α ( 1 + t ) β . Almost exponentially localized polynomial elements (needlets) φ ξ , ψ ξ are constructed and, in complete analogy with the classical case on ℝⁿ, it is shown that weighted Triebel-Lizorkin and Besov spaces can be characterized by the size of the needlet coefficients f , φ ξ in respective sequence spaces.

Nevanlinna algebras

A. Haldimann, H. Jarchow (2001)

Studia Mathematica

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The Nevanlinna algebras, α p , of this paper are the L p variants of classical weighted area Nevanlinna classes of analytic functions on = z ∈ ℂ: |z| < 1. They are F-algebras, neither locally bounded nor locally convex, with a rich duality structure. For s = (α+2)/p, the algebra F s of analytic functions f: → ℂ such that ( 1 - | z | ) s | f ( z ) | 0 as |z| → 1 is the Fréchet envelope of α p . The corresponding algebra s of analytic f: → ℂ such that s u p z ( 1 - | z | ) s | f ( z ) | < is a complete metric space but fails to be a topological vector space....

On the isomorphism classes of weighted spaces of harmonic and holomorphic functions

Wolfgang Lusky (2006)

Studia Mathematica

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Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of H v = f : Ω h o l o m o r p h i c : s u p z Ω | f ( z ) | v ( z ) < and investigate some isomorphism classes of h v = f : Ω h a r m o n i c : s u p z Ω | f ( z ) | v ( z ) < where v is a given radial weight function. Our main results show that, without any further condition on v, there are only two possibilities for Hv, namely either H v l or H v H , and at least two possibilities for hv, again h v l and h v H . We also discuss many new examples of weights.

A note on integer translates of a square integrable function on ℝ

Maciej Paluszyński (2010)

Colloquium Mathematicae

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We consider the subspace of L²(ℝ) spanned by the integer shifts of one function ψ, and formulate a condition on the family ψ ( · - n ) n = - , which is equivalent to the weight function n = - | ψ ̂ ( · + n ) | ² being > 0 a.e.

A note on the weighted Khintchine-Groshev Theorem

Mumtaz Hussain, Tatiana Yusupova (2014)

Journal de Théorie des Nombres de Bordeaux

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Let W ( m , n ; ψ ̲ ) denote the set of ψ 1 , ... , ψ n –approximable points in m n . The classical Khintchine–Groshev theorem assumes a monotonicity condition on the approximating functions ψ ̲ . Removing monotonicity from the Khintchine–Groshev theorem is attributed to different authors for different cases of m and n . It can not be removed for m = n = 1 as Duffin–Schaeffer provided the counter example. We deal with the only remaining case m = 2 and thereby remove all unnecessary conditions from the Khintchine–Groshev theorem. ...

Cardinal invariants for κ-box products: weight, density character and Suslin number

W. W. Comfort, Ivan S. Gotchev

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The symbol ( X I ) κ (with κ ≥ ω) denotes the space X I : = i I X i with the κ-box topology; this has as base all sets of the form U = i I U i with U i open in X i and with | i I : U i X i | < κ . The symbols w, d and S denote respectively the weight, density character and Suslin number. Generalizing familiar classical results, the authors show inter alia: Theorem 3.1.10(b). If κ ≤ α⁺, |I| = α and each X i contains the discrete space 0,1 and satisfies w ( X i ) α , then w ( X κ ) = α < κ . Theorem 4.3.2. If ω κ | I | 2 α and X = ( D ( α ) ) I with D(α) discrete, |D(α)| = α, then d ( ( X I ) κ ) = α < κ . Corollaries 5.2.32(a)...