Weighted estimates of certain variable kernel operators on generalized Morrey spaces with variable exponent

Let T be the singular integral operator with variable kernel and D-gamma(0 <= gamma <= 1) be the fractional differentiation operator. Simultaneously, let T* and T-# be the adjoint and pseudo-adjoint of T, T1T2 and T-1 degrees T-2 be the product and pseudo-product of T-1 and T-2 respectively. In this article, we show that, TD gamma-(DT)-T-gamma, (T*-T-#)D-gamma and (T-1 circle T-2-T1T2)D-gamma on the variable exponent generalized weighted Morrey spaces are bounded. (c) 2024 Elsevier Masson SAS. All rights are reserved, including those for text and data mining, AI training, and similar technologies.