On dilation operators in Besov spaces
نویسنده
چکیده
We consider dilation operators Tk : f → f(2·) in the framework of Besov spaces B p,q(R ) when 0 < p ≤ 1. If s > n ` 1 p − 1 ́ , Tk is a bounded linear operator from B p,q(R ) into itself and there are optimal bounds for its norm. We study the situation on the line s = n `
منابع مشابه
The Dilation Property of Modulation Spaces and Their Inclusion Relation with Besov Spaces
We consider the dilation property of the modulation spaces M. Let Dλ : f(t) 7→ f(λt) be the dilation operator, and we consider the behavior of the operator norm ‖Dλ‖Mp,q→Mp,q with respect to λ. Our result determines the best order for it, and as an application, we establish the optimality of the inclusion relation between the modulation spaces and Besov space, which was proved by Toft [9].
متن کاملHolomorphic Besov Spaces on Bounded Symmetric Domains, II
The paper continues the study of a class of holomorphic Besov spaces on bounded symmetric domains which was initiated in [18]. Several new descriptions of these Besov spaces are given in terms of weighted Bergman projections and fractional differential operators. These new characterizations are then applied to obtain results about the duality of, and Hankel operators on, weighted Bergman spaces...
متن کاملCompactly Supported Reenable Distributions in Triebel-lizorkin Spaces and Besov Spaces
The aim of this paper is to characterize compactly supported re-nable distributions in Triebel-Lizorkin spaces and Besov spaces by projection operators on certain wavelet space and by some operators on a nitely dimensional space.
متن کاملLayer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces
This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted L classes. We establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solv...
متن کاملEntropy Numbers of Trudinger–strichartz Embeddings of Radial Besov Spaces and Applications
The asymptotic behaviour of entropy numbers of Trudinger–Strichartz embeddings of radial Besov spaces on Rn into exponential Orlicz spaces is calculated. Estimates of the entropy numbers as well as estimates of entropy numbers of Sobolev embeddings of radial Besov spaces are applied to spectral theory of certain pseudo-differential operators.
متن کامل