Convolution with Odd Kernels Having a Tempered Singularity
Ron Kerman · Canadian Mathematical Bulletin · 1988
Abstract Suppose b(t) decreases to 0 on [1, ∞). Define the singular integral operator Cb at periodic f of period 1 in L1 (T),T = ( - 1 / 2, 1/2), by Then, for a large class of b one has the rearrangement inequality This inequality is used to construct a rearrangement invariant function space X corresponding to a given such space Y so that Cb maps X into Y.