𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Fourier multipliers on power-weighted Hardy spaces

✍ Scribed by T. S. Quek

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
213 KB
Volume
281
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Using Herz spaces, we obtain a sufficient condition for a bounded measurable function on ℝ^n^ to be a Fourier multiplier on H^p^~α~ (ℝ^n^ ) for 0 < p < 1 and –n < α ≤ 0. Our result is sharp in a certain sense and generalizes a recent result obtained by Baernstein and Sawyer. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Weighted Composition Operators on Hardy
Weighted Composition Operators on Hardy Spaces
✍ Manuel D Contreras; Alfredo G Hernández-Dı́az 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 94 KB

Let , be analytic functions defined on ‫,ބ‬ such that ‫ބ‬ : ‫.ބ‬ The operator Ž . given by f ¬ f ( is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continu-Ž . ity of weighted composition operators on Hardy spaces H 1

Isometric composition operators on the w
Isometric composition operators on the weighted Hardy spaces
✍ Nizar Jaoua 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 96 KB 👁 1 views

## Abstract We investigate the composition operators on the weighted Hardy spaces __H__^2^(__β__). For any bounded weight sequence __β__, we give necessary conditions for those operators to be isometric. The sufficiency of those conditions is well‐known for the classical space __H__^2^. In the case

A note on operator-valued Fourier multip
A note on operator-valued Fourier multipliers on Besov spaces
✍ Shangquan Bu; Jin-Myong Kim 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 134 KB 👁 1 views

## Abstract Let __X__ be a Banach space. We show that each __m__ : ℝ \ {0} → __L__ (__X__ ) satisfying the Mikhlin condition sup~__x__ ≠0~(‖__m__ (__x__ )‖ + ‖__xm__ ′(__x__ )‖) < ∞ defines a Fourier multiplier on __B__ ^__s__^ ~__p,q__~ (ℝ; __X__ ) if and only if 1 < __p__ < ∞ and __X__ is isomorp

Operator–valued Fourier multiplier theor
Operator–valued Fourier multiplier theorems on Besov spaces
✍ Maria Girardi; Lutz Weis 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 265 KB 👁 1 views

## Abstract Presented is a general Fourier multiplier theorem for operator–valued multiplier functions on vector–valued Besov spaces where the required smoothness of the multiplier functions depends on the geometry of the underlying Banach space (specifically, its Fourier type). The main result cov

On the Riemann Summability of Fourier In
On the Riemann Summability of Fourier Integrals and Real Hardy Spaces
✍ Ferenc Móricz 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 213 KB 👁 2 views

We consider the Riemann means of single and multiple Fourier integrals of functions belonging to L 1 or the real Hardy spaces defined on IR n , where n ≥ 1 is an integer. We prove that the maximal Riemann operator is bounded both from H 1 (IR) into L 1 (IR) and from L 1 (IR) into weak -L 1 (IR). We