Representing and interpolating sequences on parabolic Bloch type spaces

Abstract

Let H be the upper half-space of the Euclidean space. The α-parabolic Bloch type space $¥cal B$_α(σ) on H is the set of all solutions u of the parabolic equation (∂/∂t + (−Δ_x)^α)u = 0 with 0 < α ≤ 1 which belong to C¹(H) and have finite Bloch norm with weight t^σ. In this paper, we study representing and interpolating sequences on parabolic Bloch type spaces. In our previous paper [8], the reproducing formula on $¥cal B$_α(σ) is given. A representing sequence gives a discrete version of the reproducing formula on $¥cal B$_α(σ). Interpolating sequences are closely related to representing sequences, and such sequences are very interesting in their own right.