Transference of Vector-valued Multipliers on Weighted L-P-spaces
(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:
https://lup.lub.lu.se/record/3931428
- author
- Blasco, Oscar and Villarroya Alvarez, Francisco LU
- organization
- publishing date
- 2013
- 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}}, }