The behavior of the heat operator on weighted Sobolev spaces

Hile, G.; Mawata, C.

doi:10.1090/S0002-9947-98-02140-0

The behavior of the heat operator on weighted Sobolev spaces
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by G. N. Hile and C. P. Mawata PDF

Trans. Amer. Math. Soc. 350 (1998), 1407-1428 Request permission

Abstract:

Denoting by ${\mathcal {H}}$ the heat operator in $R^{n+1}$, we investigate its properties as a bounded operator from one weighted Sobolev space to another. Our main result gives conditions on the weights under which ${\mathcal {H}}$ is an injection, a surjection, or an isomorphism. We also describe the range and kernel of ${\mathcal {H}}$ in all the cases. Our results are analogous to those obtained by R. C. McOwen for the Laplace operator in $R^{n}$.

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