Advanced Studies in Pure Mathematics

Sobolev's imbedding theorem in the limiting case with Lorentz space and BMO

Hideo Kozono, Kouei Minamidate, and Hidemitsu Wadade

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Abstract

We shall prove a Gagliardo-Nirenberg type interpolation inequality with Lorentz space and BMO of functions of bounded mean oscillation in the critical case. Moreover, we obtain a Trudinger type inequality and a Brezis-Gallouet-Wainger type inequality as an application of the Gagliardo-Nirenberg type inequality.

Article information

Source
Asymptotic Analysis and Singularities — Hyperbolic and dispersive PDEs and fluid mechanics, H. Kozono, T. Ogawa, K. Tanaka, Y. Tsutsumi and E. Yanagida, eds. (Tokyo: Mathematical Society of Japan, 2007), 159-167

Dates
Received: 5 November 2005
Revised: 10 February 2006
First available in Project Euclid: 16 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1545000590

Digital Object Identifier
doi:10.2969/aspm/04710159

Mathematical Reviews number (MathSciNet)
MR2387231

Zentralblatt MATH identifier
1141.46315

Citation

Kozono, Hideo; Minamidate, Kouei; Wadade, Hidemitsu. Sobolev's imbedding theorem in the limiting case with Lorentz space and BMO. Asymptotic Analysis and Singularities — Hyperbolic and dispersive PDEs and fluid mechanics, 159--167, Mathematical Society of Japan, Tokyo, Japan, 2007. doi:10.2969/aspm/04710159. https://projecteuclid.org/euclid.aspm/1545000590


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