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On the boundedness of some potential‐type operators with oscillating kernels
Author(s) -
Karasev Denis N.,
Nogin Vladimir A.
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310258
Subject(s) - mathematics , gravitational singularity , bounded function , type (biology) , infinity , bounded mean oscillation , oscillation (cell signaling) , plane (geometry) , unit sphere , pure mathematics , regular polygon , class (philosophy) , mathematical analysis , complex plane , operator (biology) , geometry , ecology , biochemistry , chemistry , genetics , repressor , artificial intelligence , computer science , transcription factor , gene , biology
We consider a class of multidimensional potential‐type operators with kernels that have singularities at the origin and on the unit sphere and that are oscillating at infinity. We describe some convex sets in the (1/ p, 1/ q )‐plane for which these operators are bounded from L p into L q and indicate domains where they are not bounded. We also reveal some effects which show that oscillation and singularities of the kernels may strongly influence on the picture of boundedness of the operators under consideration. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)