Martingale Morrey-Hardy and Campanato-Hardy Spaces

Weighted Hardy and singular operators in Morrey spaces

We study the weighted boundedness of the Cauchy singular integral operator SΓ in Morrey spaces L(Γ) on curves satisfying the arc-chord condition, for a class of ”radial type” almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces L(0, ...

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