Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in hardy type spaces

The aim of the paper is twofold. First, we present a new general approach to the definition of a class of mixed norm spaces of analytic functions A(q;X)(D), 1 <= q < infinity on the unit disc D. We study a problem of boundedness of Bergman projection in this general setting. Second, we apply this general approach for the new concrete cases when X is either Orlicz space or generalized Morrey space, or generalized complementary Morrey space. In general, such introduced spaces are the spaces of functions which are in a sense the generalized Hadamard type derivatives of analytic functions having l(q) summable Taylor coefficients.Russian Fund of Basic Research [15-01-02732]; SFEDU grant [07/2017-31]info:eu-repo/semantics/publishedVersio

Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture

We prove two-weight norm inequalities for Calderón-Zygmund singular integrals that are sharp for the Hilbert transform and for the Riesz transforms. In addition, we give results for the dyadic square function and for commutators of singular integrals. As an application we give new results for the Sarason conjecture on the product of unbounded Toeplitz operators on Hardy spaces.Stewart Faculty Development Fund (Trinity College)Ministerio de Educación y Cienci

Variable exponent Fock spaces

summary:We introduce variable exponent Fock spaces and study some of their basic properties such as boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality. We also prove that under the global log-Hölder condition, the variable exponent Fock spaces coincide with the classical ones