Continuity of the Generalized Spherical Means Maximal Operator on Sobolev Spaces

Abstract

Let M^α be the generalized spherical means maximal operator of complex order α on ℝⁿ. The authors show that when n ≥ 2, M^α is continuous on W^1,p(ℝⁿ) if Re α > 0 and max{n/(Re α + n — 1), 1} < p < ∞.

Keywords

Continuity / spherical means maximal operator / Sobolev space / 42B25 / 46E35 / 47H99

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