Abstract
Let w denote a weight in ℝn which belongs to the Muckenhoupt class A∞ and let Mw denote the uncentered Hardy–Littlewood maximal operator defined with respect to the measure w(x)dx. The sharp Tauberian constant of Mw with respect to α, denoted by Cw(α), is defined by (Formula presented.). In this paper, we show that the Solyanik estimate (Formula presented.) holds. Following the classical theme of weighted norm inequalities we also consider the sharp Tauberian constants defined with respect to the usual uncentered Hardy–Littlewood maximal operator M and a weight w: (Formula presented.). We show that we have (Formula presented.) if and only if w ∈ A∞. As a corollary of our methods we obtain a quantitative embedding of A∞ into Ap.
Original language | English |
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Pages (from-to) | 924-946 |
Number of pages | 23 |
Journal | JOURNAL OF GEOMETRIC ANALYSIS |
Volume | 26 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Apr 2016 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Doubling measure
- Halo function
- Maximal function
- Muckenhoupt weights
- Tauberian conditions