## HISHIKAWA Yôsuke, YAMADA Masahiro,

## Representing and interpolating sequences on parabolic Bloch type spaces.

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

### Fulltext

PDF### 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 |
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MSC(Secondary) | 31B10, 32A18 |

Uncontrolled Keywords | Bloch space, parabolic operator of fractional order, representing sequence, interpolating sequence |