A family of Hardy type spaces on nondoubling manifolds

Alessio Martini; Stefano Meda; Maria Vallarino

doi:10.1007/s10231-020-00956-9

A family of Hardy type spaces on nondoubling manifolds

Alessio Martini, Stefano Meda, Maria Vallarino

Mathematics

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Abstract

We introduce a decreasing one-parameter family X ^γ(M) , γ> 0 , of Banach subspaces of the Hardy–Goldberg space h ¹(M) on certain nondoubling Riemannian manifolds with bounded geometry, and we investigate their properties. In particular, we prove that X ^{1 / 2}(M) agrees with the space of all functions in h ¹(M) whose Riesz transform is in L ¹(M) , and we obtain the surprising result that this space does not admit an atomic decomposition.

Original language	English
Pages (from-to)	2061-2085
Number of pages	25
Journal	Annali di Matematica Pura ed Applicata
Volume	199
Issue number	5
DOIs	https://doi.org/10.1007/s10231-020-00956-9
Publication status	Published - 20 Feb 2020

Keywords

Atom
Exponential growth
Hardy space
Noncompact manifold
Riesz transform

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s10231-020-00956-9Licence: None: All rights reserved

MartiniA2020family
This is a post-peer-review, pre-copyedit version of an article published in Annali di Matematica Pura ed Applicata . The final authenticated version is available online at: https://doi.org/10.1007/s10231-020-00956-9
Accepted author manuscript, 478 KBLicence: None: All rights reserved

Sub-Elliptic Harmonic Analysis
Martini, A.
Engineering & Physical Science Research Council
1/01/17 → 31/12/18
Project: Research Councils

Cite this

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AB - We introduce a decreasing one-parameter family X γ(M) , γ> 0 , of Banach subspaces of the Hardy–Goldberg space h 1(M) on certain nondoubling Riemannian manifolds with bounded geometry, and we investigate their properties. In particular, we prove that X 1 / 2(M) agrees with the space of all functions in h 1(M) whose Riesz transform is in L 1(M) , and we obtain the surprising result that this space does not admit an atomic decomposition.

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KW - Exponential growth

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KW - Noncompact manifold

KW - Riesz transform

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JF - Annali di Matematica Pura ed Applicata

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A family of Hardy type spaces on nondoubling manifolds

Abstract

Keywords

ASJC Scopus subject areas

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Sub-Elliptic Harmonic Analysis

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