Boundedness of Littlewood-Paley operators relative to non-isotropic dilations

Shuichi Sato

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 2, page 337-351
  • ISSN: 0011-4642

Abstract

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We consider Littlewood-Paley functions associated with a non-isotropic dilation group on ℝ n . We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted L p spaces, 1 < p < ∞ , with weights of the Muckenhoupt class. This, in particular, generalizes a result of N. Rivière (1971).

How to cite

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Sato, Shuichi. "Boundedness of Littlewood-Paley operators relative to non-isotropic dilations." Czechoslovak Mathematical Journal 69.2 (2019): 337-351. <http://eudml.org/doc/294433>.

@article{Sato2019,
abstract = {We consider Littlewood-Paley functions associated with a non-isotropic dilation group on $\mathbb \{R\}^n$. We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted $L^p$ spaces, $1<p<\infty $, with weights of the Muckenhoupt class. This, in particular, generalizes a result of N. Rivière (1971).},
author = {Sato, Shuichi},
journal = {Czechoslovak Mathematical Journal},
keywords = {Littlewood-Paley function; non-isotropic dilation},
language = {eng},
number = {2},
pages = {337-351},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundedness of Littlewood-Paley operators relative to non-isotropic dilations},
url = {http://eudml.org/doc/294433},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Sato, Shuichi
TI - Boundedness of Littlewood-Paley operators relative to non-isotropic dilations
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 2
SP - 337
EP - 351
AB - We consider Littlewood-Paley functions associated with a non-isotropic dilation group on $\mathbb {R}^n$. We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted $L^p$ spaces, $1<p<\infty $, with weights of the Muckenhoupt class. This, in particular, generalizes a result of N. Rivière (1971).
LA - eng
KW - Littlewood-Paley function; non-isotropic dilation
UR - http://eudml.org/doc/294433
ER -

References

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