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On the images of Sobolev spaces under the Schrödinger semigroup

  • Sivaramakrishnan C , Sukumar D and Venku Naidu Dogga EMAIL logo
Published/Copyright: January 20, 2018

Abstract

In this article, we consider the Schrödinger semigroup for the Laplacian Δ on n, and characterize the image of a Sobolev space in L2(n,eu2du) under this semigroup as weighted Bergman space (up to equivalence of norms). Also we have a similar characterization for Hermite Sobolev spaces under the Schrödinger semigroup associated to the Hermite operator H on n.

Funding statement: The first author thanks University Grant Commission, India, for financial support.

Acknowledgements

The authors wish to thank G. B. Folland for giving clarification to their questions related to weighted Sobolev spaces.

References

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Received: 2016-12-03
Accepted: 2017-12-27
Published Online: 2018-01-20
Published in Print: 2019-01-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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