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Theoretical analysis demonstrates allowable parameter ranges for weighted spherical maximal functions, resolving an open harmonic analysis problem up to endpoints.
This paper is about spherical maximal functions with general dilation sets acting on functions in weighted Lᵖ(|x|^α ) L p ( | x | α ) spaces. Aside from endpoint cases, a complete description of the allowable ranges of p , α α is given in terms of the Legendre–Assouad function of the dilation set. This settles, up to endpoints, an open problem of Duoandikoetxea and Seijo.
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Fraccaroli et al. (2026) studied this question.
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