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Gagliardo–Nirenberg Inequalities with a BMO Term
Author(s) -
Strzelecki P.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306018169
Subject(s) - mathematics , sharpening , nirenberg and matthaei experiment , norm (philosophy) , pure mathematics , mathematics subject classification , inequality , term (time) , simple (philosophy) , class (philosophy) , mathematical analysis , law , physics , quantum mechanics , philosophy , epistemology , artificial intelligence , computer science , political science , computer vision
We give a simple direct proof of the interpolation inequality‖ ∇ f ‖L 2 p2 ⩽ C‖ f ‖BMO‖ f ‖W 2 , p, where 1 < p < ∞. For p = 2 this inequality was obtained by Meyer and Rivière via a different method, and it was applied to prove a regularity theorem for a class of Yang–Mills fields. We also extend the result to higher derivatives, sharpening all those cases of classical Gagliardo–Nirenberg inequalities where the norm of the function is taken in L ∞ and other norms are in L q for appropriate q > 1. 2000 Mathematics Subject Classification 46E35 (primary), 46B70 (secondary).