Multiplication between Hardy spaces and their dual spaces

Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces

Composition Operators between Bergman and Hardy Spaces

We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.

Continuous $ k $-Frames and their Dual in Hilbert Spaces

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

Weak Hardy Spaces

We provide a careful treatment of the weak Hardy spaces Hp,∞(Rn) for all indices 0 < p < ∞. The study of these spaces presents differences from the study of the Hardy-Lorentz spaces H(R) for q <∞, due to the lack of a good dense subspace of them. We obtain several properties of weak Hardy spaces and we discuss a new square function characterization for them, obtained by He [16].

Operator Valued Hardy Spaces

We give a systematic study on the Hardy spaces of functions with values in the non-commutative L-spaces associated with a semifinite von Neumann algebra M. This is motivated by the works on matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), and on the other hand, by the recent development on the non-commutative martingale inequalities. Our non-com...