Weighted Hardy-Littlewood inequality for 𝐴-harmonic tensors

Ding, Shusen

doi:10.1090/S0002-9939-97-03762-3

Weighted Hardy-Littlewood inequality for $A$-harmonic tensors
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by Shusen Ding

Proc. Amer. Math. Soc. 125 (1997), 1727-1735

DOI: https://doi.org/10.1090/S0002-9939-97-03762-3

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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

John M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1976/77), no. 4, 337–403. MR 475169, DOI 10.1007/BF00279992
J. M. Ball and F. Murat, $W^{1,p}$-quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), no. 3, 225–253. MR 759098, DOI 10.1016/0022-1236(84)90041-7
J. B. Garnett, Bounded Analytic Functions, New York, Academic Press, 1970.
G. H. Hardy and J. E. Littlewood, Some properties of conjugate functions, J. Reine Angew. Math. 167 (1932), 405–423.
Tadeusz Iwaniec, $p$-harmonic tensors and quasiregular mappings, Ann. of Math. (2) 136 (1992), no. 3, 589–624. MR 1189867, DOI 10.2307/2946602
Tadeusz Iwaniec and Adam Lutoborski, Integral estimates for null Lagrangians, Arch. Rational Mech. Anal. 125 (1993), no. 1, 25–79. MR 1241286, DOI 10.1007/BF00411477
Tadeusz Iwaniec and Gaven Martin, Quasiregular mappings in even dimensions, Acta Math. 170 (1993), no. 1, 29–81. MR 1208562, DOI 10.1007/BF02392454
T. Iwaniec and C. A. Nolder, Hardy-Littlewood inequality for quasiregular mappings in certain domains in $\textbf {R}^n$, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 267–282. MR 802488, DOI 10.5186/aasfm.1985.1030
Craig A. Nolder, A characterization of certain measures using quasiconformal mappings, Proc. Amer. Math. Soc. 109 (1990), no. 2, 349–356. MR 1013976, DOI 10.1090/S0002-9939-1990-1013976-2
Craig A. Nolder, A quasiregular analogue of a theorem of Hardy and Littlewood, Trans. Amer. Math. Soc. 331 (1992), no. 1, 215–226. MR 1036007, DOI 10.1090/S0002-9947-1992-1036007-3
C. A. Nolder, Hardy-Littlewood theorems for $A$-harmonic tensors, Illinois J. Math., to appear.
B. Stroffolini, On weakly $A$-harmonic tensors, Studia Math., 3 114 (1995), 289–301.