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Acta Mathematica Vietnamica

INTEGRAL TRANSFORMS RELATED TO THE FOURIER COSINE CONVOLUTION WITH A WEIGHT FUNCTION

NGUYEN THANH HONG, NGUYEN MINH KHOA

Abstract

We study a new class of integral transforms from Lp(R+) to Lq(R+), 1p2, p1+q1=1, related to the Fourier cosine convolution with a weight function. We obtain necessary and sufficient conditions under which the new transforms are unitary in L2(R+). A Plancherel type theorem and the boundedness of these integral operators are obtained. We also give several examples of the new transforms kernels.