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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Weighted Hardy-Littlewood inequality for $A$-harmonic tensors

Author(s): Shusen Ding
Journal: Proc. Amer. Math. Soc. 125 (1997), 1727-1735.
MSC (1991): Primary 30C65; Secondary 31B05, 58A10
MathSciNet review: 1372027
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Abstract | References | Similar articles | Additional information

Abstract: In this paper we prove a local weighted integral inequality for conjugate $A$-harmonic tensors similar to the Hardy and Littlewood integral inequality for conjugate harmonic functions. Then by using the local weighted integral inequality, we prove a global weighted integral inequality for conjugate $A$-harmonic tensors in John domains.

References:

[B]
Ball, J. M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337-403. MR 57:14788

[BM]
Ball, J. M. and Murat, F., $W^{1, p}$-quasi-convexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), 225-253. MR 87g:49011a

[G]
J. B. Garnett, Bounded Analytic Functions, New York, Academic Press, 1970.

[HL]
G. H. Hardy and J. E. Littlewood, Some properties of conjugate functions, J. Reine Angew. Math. 167 (1932), 405-423.

[I]
T. Iwaniec, $p$-harmonic tensors and quasiregular mappings, Annals of Mathematics 136 (1992), 589-624. MR 94d:30034

[IL]
T. Iwaniec and A. Lutoborski, Integral estimates for null Lagrangians, Arch. Rational Mech. Anal. 125 (1993), 25-79. MR 95c:58054

[IM]
T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Acta Math. 170 (1993), 29-81. MR 94m:30046

[IN]
T. Iwaniec and C. A. Nolder, Hardy-Littlewood inequality for quasiregular mappings in certain domains in $ R^{n}$, Ann. Acad. Sci. Fenn. Ser. A.I. Math. 10 (1985), 267-282. MR 87d:30022

[N1]
C. A. Nolder, A characterization of certain measures using quasiconformal mappings, Proc. Amer. Math. Soc., Vol. 109, 2 (1990), 349-456. MR 90i:30034

[N2]
C. A. Nolder, A quasiregular analogue of theorem of Hardy and Littlewood, Trans. Amer. Math. Soc., Vol. 331 1 (1992), 215-226. MR 92g:30026

[N3]
C. A. Nolder, Hardy-Littlewood theorems for $A$-harmonic tensors, Illinois J. Math., to appear.

[S]
B. Stroffolini, On weakly $A$-harmonic tensors, Studia Math., 3 114 (1995), 289-301. CMP 95:14

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Additional Information:

Shusen Ding
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-3027
Address at time of publication: Department of Mathematics and Statistics, University of Minnesota, Duluth, Minnesota 55812-2496
Email: sding@d.umn.edu

DOI: 10.1090/S0002-9939-97-03762-3
PII: S 0002-9939(97)03762-3
Keywords: Conjugate harmonic tensors, differential forms and the $A$-harmonic equation
Received by editor(s): May 15, 1995
Received by editor(s) in revised form: December 8, 1995
Communicated by: Theodore W. Gamelin
Copyright of article: Copyright 1997, American Mathematical Society




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