Trudinger type inequalities in

and their best exponents

Authors:
Shinji Adachi and Kazunaga Tanaka

Journal:
Proc. Amer. Math. Soc. **128** (2000), 2051-2057

MSC (1991):
Primary 46E35, 26D10

Published electronically:
November 1, 1999

MathSciNet review:
1646323

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Abstract | References | Similar Articles | Additional Information

Abstract: We study Trudinger type inequalities in and their best exponents . We show for , ( is the surface area of the unit sphere in ), there exists a constant such that

for all . Here is defined by

It is also shown that with is false, which is different from the usual Trudinger's inequalities in bounded domains.

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Additional Information

**Shinji Adachi**

Affiliation:
Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan

Email:
kazunaga@mn.waseda.ac.jp

**Kazunaga Tanaka**

Affiliation:
Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan

DOI:
https://doi.org/10.1090/S0002-9939-99-05180-1

Received by editor(s):
May 5, 1998

Received by editor(s) in revised form:
August 26, 1998

Published electronically:
November 1, 1999

Additional Notes:
The second author was partially supported by the Sumitomo Foundation (Grant No. 960354) and Waseda University Grant for Special Research Projects 97A-140, 98A-122.

Communicated by:
Christopher Sogge

Article copyright:
© Copyright 2000
American Mathematical Society