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Transference of Vector-valued Multipliers on Weighted L-P-spaces

Blasco, Oscar and Villarroya Alvarez, Francisco LU (2013) In Canadian Journal of Mathematics 65(3). p.510-543
Abstract
New transference results for Fourier multiplier operators defined by regulated symbols are presented. We prove restriction and extension of multipliers between weighted Lebesgue spaces with two different weights, which belong to a class more general than periodic weights, and two different exponents of integrability that can be below one. We also develop some ad-hoc methods that apply to weights defined by the product of periodic weights with functions of power type. Our vector-valued approach allows us to extend our results to transference of maximal multipliers and provide transference of Littlewood-Paley inequalities.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Fourier multipliers, restriction theorems, weighted spaces
in
Canadian Journal of Mathematics
volume
65
issue
3
pages
510 - 543
publisher
Canadian Mathematical Society
external identifiers
  • wos:000319033000003
  • scopus:84901952910
ISSN
0008-414X
DOI
10.4153/CJM-2012-041-0
language
English
LU publication?
yes
id
0305bde4-d5d2-4dc4-a5ae-3833b55b063d (old id 3931428)
date added to LUP
2016-04-01 14:13:40
date last changed
2022-02-27 01:33:07
@article{0305bde4-d5d2-4dc4-a5ae-3833b55b063d,
  abstract     = {{New transference results for Fourier multiplier operators defined by regulated symbols are presented. We prove restriction and extension of multipliers between weighted Lebesgue spaces with two different weights, which belong to a class more general than periodic weights, and two different exponents of integrability that can be below one. We also develop some ad-hoc methods that apply to weights defined by the product of periodic weights with functions of power type. Our vector-valued approach allows us to extend our results to transference of maximal multipliers and provide transference of Littlewood-Paley inequalities.}},
  author       = {{Blasco, Oscar and Villarroya Alvarez, Francisco}},
  issn         = {{0008-414X}},
  keywords     = {{Fourier multipliers; restriction theorems; weighted spaces}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{510--543}},
  publisher    = {{Canadian Mathematical Society}},
  series       = {{Canadian Journal of Mathematics}},
  title        = {{Transference of Vector-valued Multipliers on Weighted L-P-spaces}},
  url          = {{http://dx.doi.org/10.4153/CJM-2012-041-0}},
  doi          = {{10.4153/CJM-2012-041-0}},
  volume       = {{65}},
  year         = {{2013}},
}