Weak type bounds for rough maximal singular integrals near L1

Weak type bounds for rough maximal singular integrals near L1

In this paper it is shown that for Ω∈Llog⁡L(Sd−1), the rough maximal singular integral operator TΩ⁎ is of weak type Llog⁡log⁡L(Rd). Furthermore, for w∈A1 and Ω∈L∞(Sd−1), it is shown that TΩ⁎ is of weak type Llog⁡log⁡L(w) with weight dependence [w]A1[w]A∞log⁡([w]A∞+1), which is same as the best known...

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Veröffentlicht in:Journal of functional analysis 2023-05, Vol.284 (10), p.109881, Article 109881
Hauptverfasser: Bhojak, Ankit, Mohanty, Parasar
Format: Artikel
Sprache:eng
Schlagworte:
Rough singular integrals
Weights
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Zusammenfassung:In this paper it is shown that for Ω∈Llog⁡L(Sd−1), the rough maximal singular integral operator TΩ⁎ is of weak type Llog⁡log⁡L(Rd). Furthermore, for w∈A1 and Ω∈L∞(Sd−1), it is shown that TΩ⁎ is of weak type Llog⁡log⁡L(w) with weight dependence [w]A1[w]A∞log⁡([w]A∞+1), which is same as the best known constant for the singular integral TΩ.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2023.109881