The spectral decomposition of weighted shifts and the condition
Earl Berkson, T. A. Gillespie (1990)
Colloquium Mathematicae
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Earl Berkson, T. A. Gillespie (1990)
Colloquium Mathematicae
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Michael Lacey (2011)
Banach Center Publications
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For an L²-bounded Calderón-Zygmund Operator T acting on , and a weight w ∈ A₂, the norm of T on L²(w) is dominated by . The recent theorem completes a line of investigation initiated by Hunt-Muckenhoupt-Wheeden in 1973 (MR0312139), has been established in different levels of generality by a number of authors over the last few years. It has a subtle proof, whose full implications will unfold over the next few years. This sharp estimate requires that the A₂ character of the weight can...
Stanisław Bylka, Jan Komar (2007)
Discussiones Mathematicae Graph Theory
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This paper deals with weighted set systems (V,,q), where V is a set of indices, and the weight q is a nonnegative integer function on . The basic idea of the paper is to apply weighted set systems to formulate restrictions on intersections. It is of interest to know whether a weighted set system can be represented by set intersections. An intersection representation of (V,,q) is defined to be an indexed family of subsets of a set S such that for each E ∈ . A necessary condition...
Shi-An Han, Ze-Hua Zhou (2016)
Czechoslovak Mathematical Journal
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We investigate isometric composition operators on the weighted Dirichlet space with standard weights , . The main technique used comes from Martín and Vukotić who completely characterized the isometric composition operators on the classical Dirichlet space . We solve some of these but not in general. We also investigate the situation when is equipped with another equivalent norm.
Jan Stochel, F. H. Szafraniec (1997)
Annales Polonici Mathematici
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The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its -vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.
Xiaosha Zhou, Lanzhe Liu (2013)
Colloquium Mathematicae
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Some weighted sharp maximal function inequalities for the Toeplitz type operator are established, where are a fixed singular integral operator with non-smooth kernel or ±I (the identity operator), are linear operators defined on the space of locally integrable functions, k = 1,..., m, and . The weighted boundedness of on Morrey spaces is obtained by using sharp maximal function inequalities.
R. Demazeux (2011)
Studia Mathematica
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We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces and for 1 ≤ p,q ≤ ∞. In particular we give some estimates for the cases 1 = p ≤ q ≤ ∞ and 1 ≤ q < p ≤ ∞.
Ali Abkar (2024)
Czechoslovak Mathematical Journal
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Using partial derivatives and , 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 can be approximated in norm by polyanalytic polynomials of degree at most .
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, , S = ∂Ω in weighted -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.
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 is given. It is shown that the solution u, constructed as in Bogovski’s approach in [1], fulfills estimates in the weighted Sobolev spaces , where the weight function w is in the class of Muckenhoupt weights .
J. A. Nitsche (1975)
Publications mathématiques et informatique de Rennes
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Eve Oja, Silja Treialt (2013)
Studia Mathematica
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The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair has the λ-bounded approximation property. Then there exists a net of finite-rank operators on X such that and for all α, and and converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.
Osvaldo Capri, Carlos Segovia (1989)
Studia Mathematica
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Harry I. Miller (2007)
Bollettino dell'Unione Matematica Italiana
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The concept of statistical convergence of a sequence was first introduced by H. Fast [7] in 1951. Recently, in the literature, the concept of statistical convergence of double sequences has been studied. The main result in this paper is a theorem that gives meaning to the statement: converges statistically to if and only if "most" of the "subsequences" of converge to in the ordinary sense. The results presented here are analogue of theorems in [12], [13] and [6] and are concerned...
Dorothee D. Haroske (2011)
Banach Center Publications
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We study continuity envelopes of function spaces and 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.
Mohammad Reza Jabbarzadeh, Rana Hajipouri (2017)
Mathematica Bohemica
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First, some classic properties of a weighted Frobenius-Perron operator on as a predual of weighted Koopman operator on will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of under certain conditions.
Ferenc Móricz (2005)
Colloquium Mathematicae
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The concepts of statistical convergence of single and double sequences of complex numbers were introduced in [1] and [7], respectively. In this paper, we introduce the concept indicated in the title. A double sequence is said to be regularly statistically convergent if (i) the double sequence is statistically convergent to some ξ ∈ ℂ, (ii) the single sequence is statistically convergent to some for each fixed j ∈ ℕ ∖ ₁, (iii) the single sequence is statistically convergent...
Maritza M. Branker (2005)
Annales Polonici Mathematici
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We apply pluripotential theory to establish results in concerning uniform approximation by functions of the form wⁿPₙ where w denotes a continuous nonnegative function and Pₙ is a polynomial of degree at most n. Then we use our work to show that on the intersection of compact sections a continuous function on Σ is uniformly approximable by θ-incomplete polynomials (for a fixed θ, 0 < θ < 1) iff f vanishes on θ²Σ. The class of sets Σ expressible as the intersection of compact...
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 and the Roumieu space as intersection and union of spaces and for associated weight sequences, respectively.
Ajay K. Sharma, S. Ueki (2012)
Annales Polonici Mathematici
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We characterize compact composition operators acting on weighted Bergman-Orlicz spaces , where α > -1 and ψ is a strictly increasing, subadditive convex function defined on [0,∞) and satisfying ψ(0) = 0, the growth condition and the Δ₂-condition. In fact, we prove that is compact on if and only if it is compact on the weighted Bergman space .
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 , . These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers.
Deba P. Sinha, Anil K. Karn (2002)
Studia Mathematica
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For p ≥ 1, a subset K of a Banach space X is said to be relatively p-compact if , where p’ = p/(p-1) and . An operator T ∈ B(X,Y) is said to be p-compact if T(Ball(X)) is relatively p-compact in Y. Similarly, weak p-compactness may be defined by considering . It is proved that T is (weakly) p-compact if and only if T* factors through a subspace of in a particular manner. The normed operator ideals of p-compact operators and of weakly p-compact operators, arising from these factorizations,...
Qingying Xue (2013)
Studia Mathematica
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The following iterated commutators of the maximal operator for multilinear singular integral operators and of the multilinear fractional integral operator are introduced and studied: , , where are the smooth truncations of the multilinear singular integral operators and is the multilinear fractional integral operator, for i = 1,…,m and f⃗ = (f1,…,fm). Weighted strong and L(logL) type end-point estimates for the above iterated commutators associated with two classes of multiple...
Nowak Grzegorz (2006)
Bollettino dell'Unione Matematica Italiana
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We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove inverse approximation theorems for functions such that , where and , .
Anna Gori (2006)
Bollettino dell'Unione Matematica Italiana
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In the present paper we give a generalization to the family of Bergman Spaces with weight , of several results, obtained in [4] for the Hardy space , concerning the cyclic and hypercyclic behaviour of composition operators CW induced by a holomorphic self map of the open unit disc .
Hidemitsu Wadade (2010)
Studia Mathematica
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We present several continuous embeddings of the critical Besov space . We first establish a Gagliardo-Nirenberg type estimate , for 1 < p ≤ q < ∞, 1 ≤ ν < ρ ≤ ∞ and the weight function with 0 < r < n. Next, we prove the corresponding Trudinger type estimate, and obtain it in terms of the embedding , where the function Φ₀ of the weighted Besov-Orlicz space is a Young function of the exponential type. Another point of interest is to embed into the weighted Besov...
Ioana Ghenciu, Paul Lewis (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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Results of Emmanuele and Drewnowski are used to study the containment of c₀ in the space , as well as the complementation of the space of w*-w compact operators in the space of w*-w operators from X* to Y.
Grzegorz Lewicki
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CONTENTSChapter 0...............................................................................................................................................................................5 0.1. Introduction..................................................................................................................................................................5 0.2. Preliminary results.......................................................................................................................................................9Chapter...