On $L_{p} - L_{q}$ boundedness for convolutions with kernels having singularities on a sphere

Alexey N. Karapetyants

L_{p} - L_{q}

boundedness for convolutions with kernels having singularities on a sphere

Alexey N. Karapetyants

Studia Mathematica, Tome 147 (2001), p. 121-134 / Harvested from The Polish Digital Mathematics Library

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Résumé

For the convolution operators $A_{a}^{α}$ with symbols ${a (| ξ |) | ξ |}^{- α} e x p i | ξ |$ , 0 ≤ Re α < n, $a (| ξ |) \in L_{\infty}$ , 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 $L_{q}$ .

Publié le : 2001-01-01

Zbl 1007.42009

EUDML-ID : urn:eudml:doc:286126

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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 147 (2001) pp. 121-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-2-2/