Invertibility of some singular integral operators and a lifting theorem

Weighted Norm Inequalities for Some Singular Integral Operators

“…We could not give a necessary and sufficient condition for the one-weighted inequality, in general. The second author [11] gave a necessary and sufficient condition for that S :, ; and S :, &; are bounded below w.r.t. W. When W # HS, if S :, ; is bounded below w.r.t W, then S :, &; is also bounded below w.r.t.…”

“…The second one-weighted inequality was studied by Rochberg [10] when the weight W is in HS. Yamamoto [11] and Nakazi [7] studied it in some special cases. In Section 4 of this paper, we give a simple necessary and sufficient condition for the second one-weighted inequality for some positive constant =, when ess.inf |:&;| >0.…”

Properties of singular integral operators $S_{α,β}$

“…Some properties of S α,β related to the norm (or weighted norm), invertibility, boundedness (with weight) etc have been studied in ( [3], [4] , [5], [6], [7], [8], [9], [10], [11], [12]). Some of these results are generalizations of properties of S. In a recent paper ( [10]) the normality and selfadjointness of the operator S α,β are studied.…”