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Displaying similar documents to “Normability of gamma spaces”

An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices

Alexei Karlovich, Eugene Shargorodsky (2021)

Czechoslovak Mathematical Journal

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We show that for every p ( 1 , ) there exists a weight w such that the Lorentz Gamma space Γ p , w is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space Γ p , w and on its associate space Γ p , w ' .

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.

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.

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.

Controlling products of currents by higher powers of plurisubharmonic functions

Ahmad K. Al Abdulaali, Hassine El Mir (2020)

Czechoslovak Mathematical Journal

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We discuss the existence of the current g k T , k for positive and closed currents T and unbounded plurisubharmonic functions g . Furthermore, a new type of weighted Lelong number is introduced under the name of weight k Lelong number.

On Lagrangian systems with some coordinates as controls

Franco Rampazzo (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Let Σ be a constrained mechanical system locally referred to state coordinates ( q 1 , , q N , γ 1 , , γ M ) . Let ( γ ~ 1 γ ~ M ) ( ) be an assigned trajectory for the coordinates γ α and let u ( ) be a scalar function of the time, to be thought as a control. In [4] one considers the control system Σ γ ^ , which is parametrized by the coordinates ( q 1 , , q N ) and is obtained from Σ by adding the time-dependent, holonomic constraints γ α = γ ^ α ( t ) := γ ~ α ( u ( t ) ) . More generally, one can consider a vector-valued control u ( ) = ( u 1 , , u M ) ( ) which is directly identified with γ ^ ( ) = ( γ ^ 1 , , γ ^ M ) ( ) . If one denotes the momenta...

On control theory and its applications to certain problems for Lagrangian systems. On hyperimpulsive motions for these. II. Some purely mathematical considerations for hyper-impulsive motions. Applications to Lagrangian systems

Aldo Bressan (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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See Summary in Note I. First, on the basis of some results in [2] or [5]-such as Lemmas 8.1 and 10.1-the general (mathematical) theorems on controllizability proved in Note I are quickly applied to (mechanic) Lagrangian systems. Second, in case Σ , χ and M satisfy conditions (11.7) when 𝒬 is a polynomial in γ ˙ , conditions (C)-i.e. (11.8) and (11.7) with 𝒬 0 -are proved to be necessary for treating satisfactorily Σ 's hyper-impulsive motions (in which positions can suffer first order discontinuities)....

Perron-Frobenius operators and the Klein-Gordon equation

Francisco Canto-Martín, Håkan Hedenmalm, Alfonso Montes-Rodríguez (2014)

Journal of the European Mathematical Society

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For a smooth curve Γ and a set Λ in the plane 2 , let A C ( Γ ; Λ ) be the space of finite Borel measures in the plane supported on Γ , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on Λ . Following [12], we say that ( Γ , Λ ) is a Heisenberg uniqueness pair if A C ( Γ ; Λ ) = { 0 } . In the context of a hyperbola Γ , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets Λ of a collection of solutions to the Klein-Gordon equation. In this work, we mainly...

Note on duality of weighted multi-parameter Triebel-Lizorkin spaces

Wei Ding, Jiao Chen, Yaoming Niu (2019)

Czechoslovak Mathematical Journal

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We study the duality theory of the weighted multi-parameter Triebel-Lizorkin spaces F ˙ p α , q ( ω ; n 1 × n 2 ) . This space has been introduced and the result ( F ˙ p α , q ( ω ; n 1 × n 2 ) ) * = CMO p - α , q ' ( ω ; n 1 × n 2 ) for 0 < p 1 has been proved in Ding, Zhu (2017). In this paper, for 1 < p < , 0 < q < we establish its dual space H ˙ p α , q ( ω ; n 1 × n 2 ) .

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...

Embeddings between weighted Copson and Cesàro function spaces

Amiran Gogatishvili, Rza Mustafayev, Tuğçe Ünver (2017)

Czechoslovak Mathematical Journal

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In this paper, characterizations of the embeddings between weighted Copson function spaces Cop p 1 , q 1 ( u 1 , v 1 ) and weighted Cesàro function spaces Ces p 2 , q 2 ( u 2 , v 2 ) are given. In particular, two-sided estimates of the optimal constant c in the inequality d ( 0 0 t f ( τ ) p 2 v 2 ( τ ) d τ q 2 / p 2 u 2 ( t ) d t ) 1 / q 2 c 0 t f ( τ ) p 1 v 1 ( τ ) d τ q 1 / p 1 u 1 ( t ) d t 1 / q 1 , d where p 1 , p 2 , q 1 , q 2 ( 0 , ) , p 2 q 2 and u 1 , u 2 , v 1 , v 2 are weights on ( 0 , ) , are obtained. The most innovative part consists of the fact that possibly different parameters p 1 and p 2 and possibly different inner weights v 1 and v 2 are allowed. The proof is based on the combination of duality techniques...

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.

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.