Hokkaido Mathematical Journal

HISHIKAWA Yôsuke, YAMADA Masahiro,

Representing and interpolating sequences on parabolic Bloch type spaces.

Hokkaido Mathematical Journal, 41 (2012) pp.335-364

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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 + (-Δx)α)u = 0 with 0 < α ≤ 1 which belong to C1(H) and have finite Bloch norm with weight tσ. 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.

MSC(Primary)35K05
MSC(Secondary)31B10, 32A18
Uncontrolled KeywordsBloch space, parabolic operator of fractional order, representing sequence, interpolating sequence