Weighted Spaces Research Articles

Tensor Products of Non-Archimedean Weighted Spaces of Continuous Functions

Abstract It is shown that the completion of the tensor product of two non-Archimedean weighted spaces of continuous functions is topologically isomorphic to another weighted space. Several applications of this result are given.

Tensor Products of Non-Archimedean Weighted Spaces of Continuous Functions

It is shown that the completion of the tensor product of two non-Archimedean weighted spaces of continuous functions is topo- logically isomorphic to another weighted space. Several applications of this result are given.

Weighted Spaces of Holomorphic Functions on Finitely Connected Domains

Mathematische NachrichtenVolume 189, Issue 1 p. 179-193 Article Weighted Spaces of Holomorphic Functions on Finitely Connected Domains Päivi Mattila, Päivi Mattila Steniuksentie 21 A 6 00320 Helsinki FinlandSearch for more papers by this author Päivi Mattila, Päivi Mattila Steniuksentie 21 A 6 00320 Helsinki FinlandSearch for more papers by this author First published: 11 November 2006 https://doi.org/10.1002/mana.19981890112Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume189, Issue11998Pages 179-193 RelatedInformation

Littlewood–Paley and Multiplier Theorems on Weighted Spaces over Locally Compact Vilenkin Groups

We extend the Littlewood–Paley theorem toLpw(G), whereGis a locally compact Vilenkin group andware weights satisfying the MuckenhouptApcondition. As an application we obtain a mixed-norm type multiplier result onLpw(G) and prove the sharpness of our result. We also obtain a sufficient condition for φ∈L∞(Γ) to be a multiplier on the power weightedLpα(G) in terms of its smoothness condition.

The Smoothness of Solutions to Nonlinear Weakly Singular Integral Equations

The differential properties of a solution of a nonlinear multidimensional weakly singular integral equation of the Uryson type on an open bounded set G \in \mathbb R^n are examined. Showing that the solution belongs to special weighted space of smooth functions, the growth of the derivatives near the boundary is described.

Multiplication Operators and Dynamical Systems on Weighted Spaces of Cross-Sections

Let $Y$ be a Hausdorff topological space, let $V$ be a system of weights on $Y$, and let $L{V_0}(Y)$ and $L{V_b}(Y)$ be the weighted locally convex spaces of cross-sections with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper, we characterise the multiplication operators on the spaces $L{V_0}(Y)$ and $L{V_b}(Y)$ induced by the scalar-valued, the vector-valued, and the operator-valued mappings. A (linear) dynamical system on the weighted spaces of cross-sections is obtained as an application of the theory of the multiplication operators. Many examples are given to illustrate the theory.

The Ap condition and a positive, linear operator

SynopsisA positive, linear operator is exhibited which is bounded on the mixed weighted Lebesgue space if and only if the weight w satisfies the Ap condition of Muckenhoupt.

A Representation Theorem for Biequicontinuous Completed Tensor Products of Weighted Spaces

A Representation Theorem for Biequicontinuous Completed Tensor Products of Weighted Spaces