θ-Summation and Hardy Spaces

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...

Hardy spaces for the strip

In this paper we present some new results about the conformally invariant Hardy spaces Hp(S) in the strip S := { z ∈ C | | Imz | < 1 } for 0 < p <∞ . We give an intrinsic characterization of these spaces and we prove that the set of polynomials are dense in all of them.

Hardy Inequalities in Function Spaces

Removable singularities for Hardy spaces

In this paper we study removable singularities for Hardy spaces of analytic functions on general domains. Two different definitions are given. For compact sets they turn out to be equal and moreover independent of the surrounding domain, as was proved by D. A. Hejhal. For non-compact sets the difference between the definitions is studied. A survey of the present knowledge is given, except for t...