Inequalities for Differential Forms

Inequalities for Differential Forms

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This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.... parabolic problems with anisotropic data spaces (translation of theoretical and numerical problems of mathematical physics (Russian), 3a€”19, aquot;Naukaaquot; , Sibirsk. ... B. Bojarski, Remarks on the stability of reverse Holder inequalities and qua- siconformal mappings, Ann. Acad. ... The one-sided minimal operator and the one-sided reverse Holder inequality, Studia Math., 116 (1995), 255-270. ... M. Goldberg, Matrix Ap weights via maximal functions, Pacific J. Math., 211 (2003), 201-220.


Title:Inequalities for Differential Forms
Author: Ravi P. Agarwal, Shusen Ding, Craig Nolder
Publisher:Springer Science & Business Media - 2009-09-19
ISBN-13:

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