Title: Sparse domination of singular integral operators. Abstract: Singular integral operators, which are a priori signed and non-local, can be dominated  in norm, pointwise, or dually, by sparse averaging operators,  which are in contrast positive and localized. The most striking consequence is that weighted norm inequalities for the singular integral follow from the corresponding, rather

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