Nearly Uniform Convergence And Interchange Of Limits
We give some necessary and sufficient conditions for an n-1 times differentiable function to be a generalized convex function with respect to an unrestricted n-parameter family.
We prove necessary and sufficient conditions for the validity of the classical chain rule in the Sobolev space and in the space of functions of bounded variation.
Let be a holomorphic function and a holomorphic self-map of the open unit disk in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators from Zygmund type spaces to Bloch type spaces in in terms of , , their derivatives, and , the -th power of . Moreover, we obtain some similar estimates for the essential norms of the operators , from which sufficient and necessary conditions of compactness of follows immediately.