On $L_p$-$L_q$ boundedness for convolutions with kernels having singularities on a sphere
Volume 144 / 2001
Studia Mathematica 144 (2001), 121-134
MSC: 31B10, 42B15, 42B20, 44A35.
DOI: 10.4064/sm144-2-2
Abstract
For the convolution operators $A_a^{\alpha }$ with symbols $a(|\xi |)|\xi |^{-\alpha }\exp {i|\xi |}$, $0\leq \mathop {\rm Re} \alpha < n$, $a(|\xi |)\in L_{\infty }$, we construct integral representations and give the exact description of the set of pairs $({1/p}, {1/q})$ for which the operators are bounded from $L_p$ to $L_q$.
