Bochner-Riesz means associated with conical surfaces

Abstract

Let d(1) and d(2) be two nonnegative integers greater than 2. We study the Fourier multiplier T-lambda associated with a conical surface S = {(xi, tau) is an element of R-d1 x R-d2 : vertical bar xi vertical bar = vertical bar tau vertical bar} defined by (T lambda f) over cap(xi, tau) = (1 - vertical bar xi vertical bar(2)/vertical bar tau vertical bar(2))(+)(lambda) psi(vertical bar tau vertical bar)(f) over cap(xi, tau) is an element of R-d1 x R-d2, where psi is a smooth function defined on Ilt, that is supported in (1/2, 2). (C) 2012 Elsevier Inc. All rights reserved.