The spectral decomposition of weighted shifts and the condition
Earl Berkson, T. A. Gillespie (1990)
Colloquium Mathematicae
Similarity:
Earl Berkson, T. A. Gillespie (1990)
Colloquium Mathematicae
Similarity:
Ali Abkar (2020)
Czechoslovak Mathematical Journal
Similarity:
We study a certain operator of multiplication by monomials in the weighted Bergman space both in the unit disk of the complex plane and in the polydisk of the -dimensional complex plane. Characterization of the commutant of such operators is given.
Jan Stochel, F. H. Szafraniec (1997)
Annales Polonici Mathematici
Similarity:
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.
V.A. Rukavishnikov, E.V. Matveeva, E.I. Rukavishnikova (2018)
Communications in Mathematics
Similarity:
We study the properties of the weighted space and weighted set for boundary value problem with singularity.
O. Duman, C. Orhan (2004)
Studia Mathematica
Similarity:
Using A-statistical convergence, we prove a Korovkin type approximation theorem which concerns the problem of approximating a function f by means of a sequence Tₙ(f;x) of positive linear operators acting from a weighted space into a weighted space .
Liang Zhang, Hui-Qiang Lu, Xiao-Mei Fu, Ze-Hua Zhou (2017)
Czechoslovak Mathematical Journal
Similarity:
Let be a locally compact group and let Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space in terms of the weights. Sufficient...
Amiran Gogatishvili, Luboš Pick, Filip Soudský (2014)
Studia Mathematica
Similarity:
We characterize associate spaces of weighted Lorentz spaces GΓ(p,m,w) and present some applications of this result including necessary and sufficient conditions for a Sobolev-type embedding into .
Eva A. Gallardo-Gutiérrez, Jonathan R. Partington (2013)
Annales de l’institut Fourier
Similarity:
A generalization of the Aleksandrov operator is provided, in order to represent the adjoint of a weighted composition operator on by means of an integral with respect to a measure. In particular, we show the existence of a family of measures which represents the adjoint of a weighted composition operator under fairly mild assumptions, and we discuss not only uniqueness but also the generalization of Aleksandrov–Clark measures which corresponds to the unweighted case, that is, to the...
Cao Jiang, Shi-An Han, Ze-Hua Zhou (2020)
Czechoslovak Mathematical Journal
Similarity:
This paper identifies a class of complex symmetric weighted composition operators on that includes both the unitary and the Hermitian weighted composition operators, as well as a class of normal weighted composition operators identified by Bourdon and Narayan. A characterization of algebraic weighted composition operators with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional. ...
Michael Lacey (2011)
Banach Center Publications
Similarity:
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...
Ming-Yi Lee (2012)
Studia Mathematica
Similarity:
Let w be in the Muckenhoupt weight class. We show that the Riesz transforms are bounded on the weighted Carleson measure space , the dual of the weighted Hardy space , 0 < p ≤ 1.
Yu-Xia Liang, Chang-Jin Wang, Ze-Hua Zhou (2015)
Annales Polonici Mathematici
Similarity:
Let H() denote the space of all holomorphic functions on the unit ball ⊂ ℂⁿ. Let φ be a holomorphic self-map of and u∈ H(). The weighted composition operator on H() is defined by . We investigate the boundedness and compactness of induced by u and φ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.
Sandra Pot (2007)
Studia Mathematica
Similarity:
Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space . We show that if W and its inverse both satisfy a matrix reverse Hölder property introduced by Christ and Goldberg, then the weighted Hilbert transform and also all weighted dyadic martingale transforms are bounded. We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform.
Stanisław Bylka, Jan Komar (2007)
Discussiones Mathematicae Graph Theory
Similarity:
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...
R. Demazeux (2011)
Studia Mathematica
Similarity:
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 ≤ ∞.
Wojciech M. Zajączkowski (2010)
Applicationes Mathematicae
Similarity:
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.
Sijue Wu (1995)
Studia Mathematica
Similarity:
We prove a T1 theorem and develop a version of Calderón-Zygmund theory for ω-CZO when .
Xiaosha Zhou, Lanzhe Liu (2013)
Colloquium Mathematicae
Similarity:
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.
Ajay K. Sharma, S. Ueki (2012)
Annales Polonici Mathematici
Similarity:
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 .
Wojciech M. Zajączkowski (2009)
Applicationes Mathematicae
Similarity:
The existence of solutions to the elliptic problem rot v = w, div v = 0 in Ω ⊂ ℝ³, , S = ∂Ω, in weighted Hilbert spaces is proved. It is assumed that Ω contains an axis L and the weight is a negative power of the distance to the axis. The main part of the proof is devoted to examining solutions in a neighbourhood of L. Their existence in Ω follows by regularization.
Alfred Witkowski (2004)
Colloquium Mathematicae
Similarity:
The author gives a new simple proof of monotonicity of the generalized extended mean values introduced by F. Qi.
Dorothee D. Haroske (2008)
Banach Center Publications
Similarity:
We study weighted function spaces of Lebesgue, Besov and Triebel-Lizorkin type where the weight function belongs to some Muckenhoupt class. The singularities of functions in these spaces are characterised by means of envelope functions.
Vakhtang Kokilashvili, Alexander Meskhi (2006)
Banach Center Publications
Similarity:
Necessary and sufficient conditions governing two-weight norm estimates for multiple Hardy and potential operators are presented. Two-weight inequalities for potentials defined on nonhomogeneous spaces are also discussed. Sketches of the proofs for most of the results are given.
Dorothee D. Haroske, Philipp Skandera (2014)
Banach Center Publications
Similarity:
We study continuous embeddings of Besov spaces of type , where s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞, and the weight w is doubling. This approach generalises recent results about embeddings of Muckenhoupt weighted Besov spaces. Our main argument relies on appropriate atomic decomposition techniques of such weighted spaces; here we benefit from earlier results by Bownik. In addition, we discuss some other related weight classes briefly and compare corresponding results.
Ramesh P. PATHAK, Shiv Kumar SAHOO (2015)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Similarity:
This paper we introducing a new sequence of positive q-integral new Modified q-Szász-Mirakyan Operators. We show that it is a weighted approximation process in the polynomial space of continuous functions defined on . Weighted statistical approximation theorem, Korovkin-type theorems for fuzzy continuous functions, an estimate for the rate of convergence and some properties are also obtained for these operators.
Maria Nowak, Renata Rososzczuk (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
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.
Pascal Lefèvre (2009)
Studia Mathematica
Similarity:
We estimate the essential norm of a weighted composition operator relative to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.