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ISSN 1088-6850(e) ISSN 0002-9947(p)

The behavior of the heat operator on weighted Sobolev spaces

Author(s): G. N. Hile; C. P. Mawata
Journal: Trans. Amer. Math. Soc. 350 (1998), 1407-1428.
MSC (1991): Primary 35B45; Secondary 35A05, 35J60
MathSciNet review: 1467466
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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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