Mathematische Nachrichten· 2026Q1
Lacunary δ‐Discretized Spherical Maximal Operators
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- Q1SCImago
- 2026year
Short summary
New lacunary δ-discretized spherical maximal operators are shown to be bounded on L^p spaces for p > 1, with endpoint weak-type estimates, and their multi-parameter variants are also bounded.
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Key points
- Introduced lacunary δ-discretized spherical maximal operators.
- Established L^p boundedness for p > 1.
- Proved endpoint weak-type estimates.
- Showed boundedness for multi-parameter variants.
- Constants are uniform in δ, recovering classical results in the limit.
AI-generated from the title and abstract; the full text is not read.
Abstract
ABSTRACT We study the lacunary analog of the ‐discretized spherical maximal operators introduced by Hickman and Jančar, for , and establish the boundedness on for all , along with the endpoint weak‐type estimate . We also prove the corresponding boundedness for the multi‐parameter variant. The constants in these bounds are uniform in , and thus, by taking the limit , our results recover the classical boundedness of the lacunary spherical maximal function.
The authors' abstract, as published at the source. Mathematische Nachrichten, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics