Hormander’s Condition for Multilinear Fourier Multipliers ABSTRACT: Let m be a positive integer. In this talk, we will introduce optimal conditions, expressed in terms of Sobolev spaces, on m-linear Fourier multiplier operators to be bounded from a product of Lebesgue or Hardy spaces to Lebesgue spaces. Our results are sharp and cover the bilinear case (m

Title:Contact and symplectic geometry in low dimensions Abstract: This series of talks will be about explaining some fundamental open problems in three-dimensional contact geometry. The first talk will be devoted to a gentle introduction to low dimensional contact and symplectic topology: some of the important problems that have been shaping much of current research, and

Title: Fractional Integral Operators Associated to Schrodinger Operators Abstract: Consider the Schroedinger operator Lf(x) = - Laplace f(x) + V(x)f(x). We investigate weighted inequalities for the fractional integral operator I_a = (L)^-a/2. More precisely, let 0 < a < n and 1/p - 1/q = a/n, we would like to estimate the operator norm of

Conde-Alonso, Jos´e Manuel (Universitat Aut`onoma de Barcelona, Spain):  A dyadic RBMO space and pointwise domination of nonhomogeneous Calder´on- Zygmund operators. Abstract: We revisit basic nonhomogeneous Caldero´n-Zygmund theory from the point of view of martingales. Given a measure µ of polynomial growth on Rd, we refine a deep result by David and Mattila to construct an

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.