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Two-Weighted Intergal Inequalities for Differential Forms

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In this paper, we make use of the weight to obtain some two-weight integral inequalities which are generalizations of the Poincar´e inequality. These inequalities are extensions of classical results and can be used to study the integrability of differential forms and to estimate the integrals of differential forms. Finally, we give some applications of this results to quasiregular mappings.

Abstract

In this paper, we make use of the weight to obtain some two-weight integral inequalities which are generalizations of the Poincar´e inequality. These inequalities are extensions of classical results and can be used to study the integrability of differential forms and to estimate the integrals of differential forms. Finally, we give some applications of this results to quasiregular mappings.

참고문헌 (14)

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  2. J. M. Ball, ";p-quasi-Convexity and Variational Problems for Multiple Integrals", J. Funct. Anal, 58, pp.225~253 (1984)
  3. T. Iwaniec, "p-Harmonic Tensors and Quasiregular Mappings", Ann. Math, 136, pp.589~624 (1992)
  4. T. Iwaniec, "Quasiregular Mappings in Even Dimensions", Acta Math, 170, pp.29~81 (1993)
  5. C. A. Nolder, "Hardy-Littlewood Theorems for A-Harmonic Tensors", Illinois J. Math. Anal. Appl, 43, pp.613~631 (1999)
  6. B. Stro olini, "On Weakly A-Harmonic Tensors", Studia Math, 114(3), pp.289~301 (1995)
  7. J. B. Garnett, "Bounded Analytic Functions" (1970), Academic Press
  8. J. Heinonen, "Nonlinear Potential Theory of Degenerate Elliptic Equations" (1993), Clarendon Press
  9. S. Ding, "Weighted Norm Inequalities for Conjugate A-Harmonic Tensors", J. Math. Anal. Appl, 203, pp.279~289 (1996)
  10. S. Ding, "Estimates of Weighted Integrals for Di erential Forms", J. Math. Anal. Appl, 256, pp.312~323 (2001)
  11. S. Ding, "Weighted Poincare-Type Inequalities for Di erential Forms in Ls()- Averaging Domains", J. Math. Anal. Appl, 227, pp.200~215 (1998)
  12. S. Ding, "Weak Reverse Holder Inequalities and Imbedding Inequalities for Solutions to the A-Harmonic Equation", Non. Anal, 51, pp.789~800 (2002)
  13. S. Ding, "Weighted Integral Inequalities for Solutions to the A-Harmonic Equations", ~, to appear
  14. B. Bojarski, "Analytical foundations of the theory of quasiconformal mappings in Rn", Ann. Acad. Sci. Fenn. Ser. AI Math, 8, pp.257~324 (1983)

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