On extremals for a Radon-like transform

Abstract

Convolution with an appropriate surface measure on a paraboloid in R^d defines a bounded operator T from L^p(R^d) to L^q(R^d) for certain exponents p,q. In this article it is proved that there exist functions which extremize the associated inequality.

References in corpus (3)

• Quasiextremals for a Radon-like transform
• Endpoint bounds for a generalized {R}adon transform
• Existence of Extremals for a Fourier Restriction Inequality

Cited by in corpus (8)

• A sharpened Hausdorff-Young inequality
• Near-extremizers of Young's Inequality for R^d
• Best constant and value of extremizers for a k-plane transform inequality
• On the extremizers of an adjoint Fourier restriction inequality
• Extremizers for Fourier restriction inequalities: convex arcs
• Existence and non-existence of extremizers for certain $k$-plane transform inequalities
• Compactness of a restricted X-ray transform
• Uniform $L_x^p-L_{x,r}^q$ Improving for Dilated Averages over Polynomial Curves