Radial maximal function characterizations for Hardy spaces on RD-spaces

Loukas Grafakos; Liguang Liu; Dachun Yang

Bulletin de la Société Mathématique de France (2009)

  • Volume: 137, Issue: 2, page 225-251
  • ISSN: 0037-9484

Abstract

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An RD-space 𝒳 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds. The authors prove that for a space of homogeneous type 𝒳 having “dimension” n , there exists a p 0 ∈ ( n / ( n + 1 ) , 1 ) such that for certain classes of distributions, the L p ( 𝒳 ) quasi-norms of their radial maximal functions and grand maximal functions are equivalent when p ∈ ( p 0 , ∞ ] . This result yields a radial maximal function characterization for Hardy spaces on 𝒳 .

How to cite

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Grafakos, Loukas, Liu, Liguang, and Yang, Dachun. "Radial maximal function characterizations for Hardy spaces on RD-spaces." Bulletin de la Société Mathématique de France 137.2 (2009): 225-251. <http://eudml.org/doc/272343>.

@article{Grafakos2009,
abstract = {An RD-space $\mathcal \{X\}$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds. The authors prove that for a space of homogeneous type $\mathcal \{X\}$ having “dimension” $n$, there exists a $p_0\in (n/(n+1), 1)$ such that for certain classes of distributions, the $L^p(\mathcal \{X\})$ quasi-norms of their radial maximal functions and grand maximal functions are equivalent when $p\in (p_0,\infty ]$. This result yields a radial maximal function characterization for Hardy spaces on $\mathcal \{X\}$.},
author = {Grafakos, Loukas, Liu, Liguang, Yang, Dachun},
journal = {Bulletin de la Société Mathématique de France},
keywords = {space of homogeneous type; approximation of the identity; space of test function; grand maximal function; radial maximal function; Hardy space},
language = {eng},
number = {2},
pages = {225-251},
publisher = {Société mathématique de France},
title = {Radial maximal function characterizations for Hardy spaces on RD-spaces},
url = {http://eudml.org/doc/272343},
volume = {137},
year = {2009},
}

TY - JOUR
AU - Grafakos, Loukas
AU - Liu, Liguang
AU - Yang, Dachun
TI - Radial maximal function characterizations for Hardy spaces on RD-spaces
JO - Bulletin de la Société Mathématique de France
PY - 2009
PB - Société mathématique de France
VL - 137
IS - 2
SP - 225
EP - 251
AB - An RD-space $\mathcal {X}$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds. The authors prove that for a space of homogeneous type $\mathcal {X}$ having “dimension” $n$, there exists a $p_0\in (n/(n+1), 1)$ such that for certain classes of distributions, the $L^p(\mathcal {X})$ quasi-norms of their radial maximal functions and grand maximal functions are equivalent when $p\in (p_0,\infty ]$. This result yields a radial maximal function characterization for Hardy spaces on $\mathcal {X}$.
LA - eng
KW - space of homogeneous type; approximation of the identity; space of test function; grand maximal function; radial maximal function; Hardy space
UR - http://eudml.org/doc/272343
ER -

References

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