Hyperbolic Hardy class $H^1$

p-Carleson Measures for a Class of Hardy-Orlicz Spaces

An alternative interpretation of a family of weighted Carleson measures is used to characterize p-Carleson measures for a class of Hardy-Orlicz spaces admitting a nice weak factorization. As an application, we provide with a characterization of symbols of bounded weighted composition operators and Cesàro-type integral operators from these Hardy-Orlicz spaces to some classical holomorphic functi...

[hal-00864457, v1] The Hardy space H1 in the rational Dunkl setting

This paper consists in a first study of the Hardy space H in the rational Dunkl setting. Following Uchiyama’s approach, we characterizee H atomically and by means of the heat maximal operator. We also obtain a Fourier multiplier theorem for H. These results are proved here in the one-dimensional case and in the product case.

On the Hermite expansions of functions from Hardy class by

Considering functions f on Rn for which both f and f̂ are bounded by the Gaussian e 1 2 a|x| , 0 < a < 1 we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for O(n)−finite functions thus extending the one dimensional result of Vemuri [11].

On the applications of Hardy class functions in scattering theory

This paper is a response to an article [26] recently published in Journal of Physics A: Mathematical and Theoretical. The article claims that the theory of resonances and decaying states based on certain rigged Hilbert spaces of Hardy functions is physically untenable. In this paper we show that all of the key conclusions of [26] are the result of either the errors in mathematical reasoning or ...

Weak Factorizations of the Hardy space H1(Rn) in terms of Multilinear Riesz Transforms