Radial Fourier multipliers in high dimensions

Yaryong Heo; Fëdor Nazarov; Andreas Seeger

doi:10.1007/s11511-011-0059-x

Radial Fourier multipliers in high dimensions

Yaryong Heo, Fëdor Nazarov, Andreas Seeger

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

Abstract

Given a fixed p≠2, we prove a simple and effective characterization of all radial multipliers of, provided that the dimension d is sufficiently large. The method also yields new L^q space-time regularity results for solutions of the wave equation in high dimensions.

Original language	English
Pages (from-to)	55-92
Number of pages	38
Journal	Acta Mathematica
Volume	206
Issue number	1
DOIs	https://doi.org/10.1007/s11511-011-0059-x
Publication status	Published - 2011 Mar

ASJC Scopus subject areas

Mathematics(all)

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title = "Radial Fourier multipliers in high dimensions",

abstract = "Given a fixed p≠2, we prove a simple and effective characterization of all radial multipliers of, provided that the dimension d is sufficiently large. The method also yields new Lq space-time regularity results for solutions of the wave equation in high dimensions.",

author = "Yaryong Heo and F{\"e}dor Nazarov and Andreas Seeger",

note = "Funding Information: Y. H. was supported by grants from the Korea Research Foundation and the National Research Foundation of Korea. F. N. and A. S. were supported in part by grants from the National Science Foundation.",

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AU - Seeger, Andreas

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N2 - Given a fixed p≠2, we prove a simple and effective characterization of all radial multipliers of, provided that the dimension d is sufficiently large. The method also yields new Lq space-time regularity results for solutions of the wave equation in high dimensions.

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Radial Fourier multipliers in high dimensions

Abstract

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