Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Sharp asymptotic estimates for a class of Littlewood-Paley operators

Bakas, Odysseas LU (2021) In Studia Mathematica 260(2). p.195-216
Abstract

It is well-known that Littlewood-Paley operators formed with respect to lacunary sets of finite order are bounded on Lp(ℝ) for all 1 < p < ∞. In this note it is shown that 'Equation Presented' where SIE2 denotes the classical Littlewood-Paley operator formed with respect to the second order lacunary set E2 = {±(2k -2l) : k, l ∈ ℤ with k > l}. Variants in the periodic setting and for certain lacunary sets of order N are also presented.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Lacunary sets of finite order, Littlewood-Paley square functions, Weighted inequalities
in
Studia Mathematica
volume
260
issue
2
pages
22 pages
publisher
Instytut Matematyczny
external identifiers
  • scopus:85111563929
ISSN
0039-3223
DOI
10.4064/sm200514-6-10
language
English
LU publication?
yes
id
4132ce80-a186-45a2-8689-e1065ee01f90
date added to LUP
2021-08-30 11:49:52
date last changed
2025-01-13 12:14:52
@article{4132ce80-a186-45a2-8689-e1065ee01f90,
  abstract     = {{<p>It is well-known that Littlewood-Paley operators formed with respect to lacunary sets of finite order are bounded on Lp(ℝ) for all 1 &lt; p &lt; ∞. In this note it is shown that 'Equation Presented' where SIE2 denotes the classical Littlewood-Paley operator formed with respect to the second order lacunary set E2 = {±(2k -2l) : k, l ∈ ℤ with k &gt; l}. Variants in the periodic setting and for certain lacunary sets of order N are also presented.</p>}},
  author       = {{Bakas, Odysseas}},
  issn         = {{0039-3223}},
  keywords     = {{Lacunary sets of finite order; Littlewood-Paley square functions; Weighted inequalities}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{195--216}},
  publisher    = {{Instytut Matematyczny}},
  series       = {{Studia Mathematica}},
  title        = {{Sharp asymptotic estimates for a class of Littlewood-Paley operators}},
  url          = {{http://dx.doi.org/10.4064/sm200514-6-10}},
  doi          = {{10.4064/sm200514-6-10}},
  volume       = {{260}},
  year         = {{2021}},
}