## 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 $R^{n}$.## References

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## Additional Information

**G. N. Hile**- Affiliation: University of Hawaii, Manoa, 2565 The Mall, Honolulu, Hawaii 96822
- Email: hile@math.hawaii.edu
**C. P. Mawata**- Affiliation: University of Tennessee, Chattanooga, 615 McCallie Avenue, Chattanooga, Tennessee 37403
- Email: cmawata@cecasun.utc.edu
- Received by editor(s): April 12, 1996
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**350**(1998), 1407-1428 - MSC (1991): Primary 35B45; Secondary 35A05, 35J60
- DOI: https://doi.org/10.1090/S0002-9947-98-02140-0
- MathSciNet review: 1467466