Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Weighted norm estimates for Sobolev spaces


Author: Martin Schechter
Journal: Trans. Amer. Math. Soc. 304 (1987), 669-687
MSC: Primary 46E35; Secondary 26D20
DOI: https://doi.org/10.1090/S0002-9947-1987-0911089-3
MathSciNet review: 911089
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give sufficient conditions for estimates of the form

$\displaystyle {\int {\left\vert {u(x)} \right\vert} ^q}d\mu (x) \leqslant C\left\Vert u \right\Vert _{s,p}^1,\qquad u \in {H^{s,p}},$

to hold, where $ \mu (x)$ is a measure and $ {\left\Vert u \right\Vert _{s,p}}$ is the norm of the Sobolev space $ {H^{s,p}}$. If $ d\mu = dx$, this reduces to the usual Sobolev inequality. The general form has much wider applications in both linear and nonlinear partial differential equations. An application is given in the last section.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E35, 26D20

Retrieve articles in all journals with MSC: 46E35, 26D20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1987-0911089-3
Article copyright: © Copyright 1987 American Mathematical Society