Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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


Author: Shusen Ding
Journal: Proc. Amer. Math. Soc. 125 (1997), 1727-1735
MSC (1991): Primary 30C65; Secondary 31B05, 58A10
DOI: https://doi.org/10.1090/S0002-9939-97-03762-3
MathSciNet review: 1372027
Full-text PDF

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 [Enhancements On Off] (What's this?)

  • [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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30C65, 31B05, 58A10

Retrieve articles in all journals with MSC (1991): 30C65, 31B05, 58A10


Additional Information

Shusen Ding
Email: sding@d.umn.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03762-3
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
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society