Geodesic
On $L_p$-$L_q$ boundedness for convolutions with kernels having singularities on a sphere
Alexey N. Karapetyants 1
1 Mathematics Department Center for Research and Advanced Study A.P. 14-740, 07000 México, D.F., México
Studia Mathematica, Tome 144 (2001) no. 2, pp. 121-134 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $L_q$.
DOI : 10.4064/sm144-2-2
Keywords: convolution operators alpha symbols alpha exp leq mathop alpha infty construct integral representations exact description set pairs which operators bounded nbsp

Alexey N. Karapetyants  1

1 Mathematics Department Center for Research and Advanced Study A.P. 14-740, 07000 México, D.F., México 
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Alexey N. Karapetyants. On $L_p$-$L_q$ boundedness for convolutions with
kernels having singularities on a sphere. Studia Mathematica, Tome 144 (2001) no. 2, pp. 121-134. doi: 10.4064/sm144-2-2

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