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On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

Radha, R and Thangavelu, S and Naidu, Venku D (2013) On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group. In: Mathematische Nachrichten, 286 (13). pp. 1337-1352.

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Official URL: http://dx.doi.org/10.1002/mana.201100233

Abstract

The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order H-m (H-n), m is an element of N-n, under the heat kernel transform on H-n, using direct sum and direct integral of Bergmann spaces and certain unitary representations of H-n which can be realized on the Hilbert space of Hilbert-Schmidt operators on L-2 (R-n). We also show that the image of Sobolev space of negative order H-s (H-n), s(> 0) is an element of R is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on H-n under the heat kernel transform. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Item Type: Journal Article
Additional Information: Copyright of this article belongs to John Wiley and Sons.
Keywords: Heisenberg Group; Sobolev Space; Sublaplacian; Hermite Functions; Semigroup
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Francis Jayakanth
Date Deposited: 06 Jan 2014 10:02
Last Modified: 06 Jan 2014 10:02
URI: http://eprints.iisc.ac.in/id/eprint/48116

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