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• W1765484778 abstract "Let $mu$ be a Radon measure on $mathbb {R}^d$, which may be nondoubling. The only condition that $mu$ must satisfy is the size condition $mu (B(x,r))leq C r^n$, for some fixed $0<nleq d$. Recently, some spaces of type $B!M!O(mu )$ and $H^1(mu )$ were introduced by the author. These new spaces have properties similar to those of the classical spaces $BMO$ and $H^1$ defined for doubling measures, and they have proved to be useful for studying the $L^p(mu )$ boundedness of Calderón-Zygmund operators without assuming doubling conditions. In this paper a characterization of the new atomic Hardy space $H^1(mu )$ in terms of a maximal operator $M_Phi$ is given. It is shown that $f$ belongs to $H^1(mu )$ if and only if $fin L^1(mu )$, $int f dmu =0$ and $M_Phi f in L^1(mu )$, as in the usual doubling situation." @default.
• W1765484778 created "2016-06-24" @default.
• W1765484778 creator A5066249414 @default.
• W1765484778 date "2002-09-11" @default.
• W1765484778 modified "2023-10-14" @default.
• W1765484778 title "The space $H^1$ for nondoubling measures in terms of a grand maximal operator" @default.
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• W1765484778 doi "https://doi.org/10.1090/s0002-9947-02-03131-8" @default.
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