The Hardy Space $$H^1$$ H 1 in the Rational Dunkl Setting

[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.

Multipliers of the Hardy space H 1 and

We study the space of functions ϕ: IN → C such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors ξ, η in H such that ϕ(n) = T n ξ, η. This implies that the matrix (ϕ(i + j)) i,j≥0 is a Schur multiplier of B(ℓ 2) or equivalently is in the space (ℓ 1 ∨ ⊗ ℓ 1) *. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach make...

Convolution Operators and Bochner-Riesz Means on Herz-Type Hardy Spaces in the Dunkl Setting

The classical theory of Hardy spaces on n has received an important impetus from the work of Fefferman and Stein, Lu and Yang 1, 2 . Their work resulted in many applications involving sharp estimates for convolution and multiplier operators. By using the technique of Herz-type Hardy spaces for the Dunkl operator Λα, we are attempting in this paper to study the Dunkl convolution operators, andwe...

On a Rational Approximation Problemin the Real Hardy Space

Constrained extremal problems in the Hardy space H 2 and

We study some approximation problems on a strict subset of the circle by analytic functions of the Hardy space H of the unit disk (in C), whose modulus satisfy a pointwise constraint on the complentary part of the circle. Existence and uniqueness results, as well as pointwise saturation of the constraint, are established. We also derive a critical point equation which gives rise to a dual formu...