On a sharp Moser–Aubin–Onofri inequality for functions on S2 with symmetry

Gui, Changfeng; Wei, Juncheng

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On a sharp Moser–Aubin–Onofri inequality for functions on S² with symmetry

Changfeng Gui and Juncheng Wei

Vol. 194 (2000), No. 2, 349–358

DOI: 10.2140/pjm.2000.194.349

Abstract

We show that for α ≥ 1
2 , the following inequality holds:

α∫ 1 2 ′ 2 ∫ 1 1∫ 1 2g(x) 2 − 1(1− x )|g (x)| dx+ −1g(x)dx− log 2 −1e dx ≥ 0,

for every function g on (−1,1) satisfying ∥g∥² = ∫ ₋₁¹(1 − x²)|g′(x)|²dx < ∞ and ∫ ₋₁¹e^2g(x)xdx = 0. This improves a result of Feldman et al., 1998, and answers a question of Chang and Yang in the axially symmetric case.

Milestones

Received: 10 September 1998

Published: 1 June 2000

Authors

Changfeng Gui
Department of Mathematics University of British Columbia Vancouver, BC V6T 1Z2 Canada

Juncheng Wei
Department of Mathematics The Chinese University of Hong Kong Shatin, Hong Kong China

Vol. 194, No. 2, 2000

Changfeng Gui and Juncheng Wei

Abstract

Milestones

Authors