Spherical maximal operators on radial functions

1996/01/01 by Seeger, Andreas, Wainger, Stephen, Wright, James · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/9601220

Abstract

Let A_tf(x)=∫ f(x+ty)dσ(y) denote the spherical means in \Bbb R^d (dσ is surface measure on S^d-1, normalized to 1). We prove sharp estimates for the maximal function M_E f(x)=sup_{t∈ E}|A_tf(x)| where E is a fixed set in \Bbb R⁺ and f is a \it radial function ∈ L^p(\Bbb R^d). Let p_d=d/(d-1) (the critical exponent of Stein's maximal function). For the cases (i) p

Cited by

• Problems on spherical maximal functions

Related

• Spherical maximal estimates via geometry
• Lp bounds for Stein's spherical maximal operators
• A note on generalized spherical maximal means
• Sparse Bounds for Spherical Maximal Functions
• Improved L^p bounds for the strong spherical maximal operator