Interpolating sequences Hp with p < 1

Interpolating Sequences in the Polydisc

Let H°°(Dn) denote the set of all bounded analytic functions defined on the polydisc D" of Cn. In this note, we give a sufficient condition for sequences of points in £>" to be interpolating sequences for H°°(Dn). We also discuss some conditions for interpolation of general domains. Let G(X) be the set of all bounded continuous functions on a compact set X and let A C C(X) be a uniform algebra ...

THE SPACE Hp WITH 0<p<l

Interpolating and Sampling Sequences for Entire Functions

We characterise interpolating and sampling sequences for the spaces of entire functions f such that fe ∈ L(C), p ≥ 1 (and some related weighted classes), where φ is a subharmonic weight whose Laplacian is a doubling measure. The results are expressed in terms of some densities adapted to the metric induced by ∆φ. They generalise previous results by Seip for the case φ(z) = |z|2, and by Berndtss...

General Interpolating Sequences for the Bergman Spaces

Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these characterizations remain valid without that condition. The general interpolation we consider here includes the usual simple interpolation and multiple interpo...

Interpolating Sequences on Analytic Besov Type Spaces

We characterize the interpolating sequences for the weighted analytic Besov spaces Bp(s), defined by the norm ‖f‖ Bp(s) = |f(0)|p + Z D |(1− |z|2)f ′(z)|p(1− |z|2)s dA(z) (1− |z|2)2 , 1 < p < ∞ and 0 < s < 1, and for the corresponding multiplier spaces M(Bp(s)).