Inequalities for Differential Forms

Cover -- Preface -- Contents -- Hardy -- Littlewood inequalities -- Differential forms -- Basic elements -- Definitions and notations -- Poincar233; lemma -- A-harmonic equations -- Quasiconformal mappings -- A-harmonic equations -- p-Harmonic equations -- Two equivalent forms -- Three-dimensional cases -- The equivalent system -- An example -- Some weight classes -- Ar()-weights -- Ar(, E)-weights -- Ar (E)-weights -- Some classes of two-weights -- Inequalities in John domains -- Local inequalities -- Weighted inequalities -- Global inequalities -- Inequalities in averaging domains -- Averaging domains -- Ls()-averaging domains -- Other weighted inequalities -- Two-weight cases -- Local inequalities -- Global inequalities -- The best integrable condition -- An example -- Remark -- Inequalities with Orlicz norms -- Norm comparison theorem -- Lp (logL)-norm inequality -- Ar()-weighted case -- Global Ls(logL)-norm inequality -- Norm comparison theorems -- Introduction -- The local unweighted estimates -- Basic Lp-inequalities -- Special cases -- The local weighted estimates -- Ls-estimates for dv -- Ls-estimates for du -- The norm comparison between d and d -- The global estimates -- Global estimates for dv -- Global estimates for du -- Global Lp-estimates -- Global Ls-estimates -- Applications -- Imbedding theorems for differential forms -- Poincar233;-type inequalities -- Introduction -- Inequalities for differential forms -- Basic inequalities -- Weighted inequalities -- Inequalities for harmonic forms -- Global inequalities in averaging domains -- Ar-weighted inequalities -- Inequalities for Green's operator -- Basic estimates for operators -- Weighted inequality for Green's operator -- Global inequality for Green's operator -- Inequalities with Orlicz norms -- Local inequality -- Weighted inequalities -- The proof of the global inequality -- Two-weight inequalities -- Statements of two-weight inequalities -- Proofs of the main theorems -- Ar()-weighted inequalities -- Inequalities for Jacobians -- Some notations -- Two-weight estimates -- Inequalities for the projection operator -- Statement of the main theorem -- Inequality for and G -- Proof of the main theorem -- Other Poincar233;-type inequalities -- Caccioppoli inequalities -- Preliminary results -- Local and global weighted cases -- Ar()-weighted inequality -- Ar(,)-weighted inequality -- Ar()-weighted inequality -- Parametric version -- Inequalities with two parameters -- Local and global two-weight cases -- An unweighted inequality -- Two-weight inequalities -- Inequalities with Orlicz norms -- Basic "026B30D "026B30D Lp(logL)(E) estimates -- Weak reverse H246;lder inequalities -- Ar(M)-weighted cases -- Inequalities with the codifferential operator -- Lq-estimate for dv -- Two-weight estimate for dv -- Imbedding theorems -- Introduction -- Quasiconformal mappings -- Solutions to the nonhomogeneous equation -- Imbedding inequalities for operators -- The gradient and homotopy operators -- Some special cases -- Global imbedding theorems -- Other weighted cases -- Ls.