Two-weight estimates for singular and strongly singular integral operators
- 84 Downloads
We consider conditional two-weight estimates for singular and strongly singular integral operators. The conditions governing two-weight estimates shall be simultaneously necessary and sufficient for quite a large class of singular integrals.
Key words and phrasessingular integrals two-weight estimates
2000 Mathematics Subject Classification42B20
Unable to display preview. Download preview PDF.
- J. Garcia-Cuerza and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North Holland (Amsterdam, New York, Oxford, 1985).Google Scholar
- I. Genebashvili, A. Gegatishvili, V. Kokilashvili and M. Krbec, Weight Theory for Integral Transforms on Spaces of Homogeneous Type, Pitman Monographs and Surveys in Pure and Applied Mathematics, 92, Longman (Harlow, 1992).Google Scholar
- E. Gusseinov, Singular integrals in the space of functions summable with monotone weight (Russian), Mat. Sb., 132(174) (1977), 28–44.Google Scholar
- Y. Hu, A Weighted Norm Inequality for Oscillatory Singular Integrals, Harmonic Analysis (Tianjin, 1988), Lecture Notes in Math., Springer Verlag (Berlin, 1994).Google Scholar
- V. Kokilashvili and A. Meskhi, Two-weight inequalities for singular integrals defined on homogeneous groups, in: Function Spaces V, Proceedings of the Conference, Poznań, Poland, M. Mudzik and L. Skrzypczak, eds., Lecture Notes in Pure and Applied Mathematics, 213, Marcel Dekker (2000).Google Scholar
- N. Lyall, A class of strongly singular Radon transforms on the Heisenberg group, to appear in Proc. of Edin. Math. Soc. Google Scholar
- V. Maz’ya, Sobolev Spaces, Springer (Berlin, 1985).Google Scholar
- S. Wainger, Special Trigonometric Series in k Dimensions, Memoirs of the AMS 59, American Math. Soc. (1965).Google Scholar