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
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $L_q$.
Keywords:
convolution operators alpha symbols alpha exp leq mathop alpha infty construct integral representations exact description set pairs which operators bounded nbsp
Affiliations des auteurs :
Alexey N. Karapetyants 1
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author = {Alexey N. Karapetyants},
title = {On $L_p$-$L_q$ boundedness for convolutions with
kernels having singularities on a sphere},
journal = {Studia Mathematica},
pages = {121--134},
publisher = {mathdoc},
volume = {144},
number = {2},
year = {2001},
doi = {10.4064/sm144-2-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm144-2-2/}
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%0 Journal Article %A Alexey N. Karapetyants %T On $L_p$-$L_q$ boundedness for convolutions with kernels having singularities on a sphere %J Studia Mathematica %D 2001 %P 121-134 %V 144 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm144-2-2/ %R 10.4064/sm144-2-2 %G en %F 10_4064_sm144_2_2
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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