VARIABLE EXPONENT BOUNDED VARIATION SPACES IN THE RIESZ SENSE Abstract This talk introduces Variable Exponent Bounded Variation Spaces in the Riesz Sense. We prove some embedding results and present a Riesz representation lemma in our setting . Also it shows an application of the latter result by characterizing the global Lipschitz Nemytskii operator on the newly introduced spaces

Title: Weighted restricted weak type inequalities Abstract: We review classical results concerning the bounds of the Hardy-Littlewood maximal operator on weighted Lorentz spaces and discuss the analogous bounds for the pointwise product of such operators. A new Hölder-type inequality for Lorentz spaces is used.

Title: Cowen-Douglas Operators and the Corona Problem Abstract: I will discuss how the recent method used in solving various form of the corona problem can be used to classify Cowen-Douglas operators up to similarity.

Title: "A Compact Embedding Theorem for Degenerate Sobolev Spaces" Abstract: In this talk I will prove a compact embedding theorem for degenerate Sobolev spaces into naturally associated weighted Lebesgue spaces. This is a generalization of the Rellich Kondrachov compactness theorem for classical Sobolev spaces.  These embeddings have been studied in a very general context in