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Johnson, Casey; Ding, Shusen

Integral estimates for the potential operator on differential forms. (English) Zbl 1285.47056

Int. J. Anal. 2013, Article ID 108623, 6 p. (2013).
The authors prove local and global weighted estimates for the potential operator applied to a class of differential forms, which includes the solutions of the \(A\)-harmonic equation, and for a new class of weights.
Reviewer: Mihai Pascu (Bucureşti)

Cited in 5 Documents

MSC:

47G40 Potential operators
47B34 Kernel operators
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
26D10 Inequalities involving derivatives and differential and integral operators
58A10 Differential forms in global analysis

Keywords:

potential operator; differential forms; integral estimates; averaging domains
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\textit{C. Johnson} and \textit{S. Ding}, Int. J. Anal. 2013, Article ID 108623, 6 p. (2013; Zbl 1285.47056)
Full Text: DOI

References:

[1] R. P. Agarwal, S. Ding, and C. A. Nolder, Inequalities for Differential Forms, Springer, New York, NY, USA, 2009. · Zbl 1253.54050
[2] H. Bi, “Weighted inequalities for potential operators on differential forms,” Journal of Inequalities and Applications, vol. 2010, Article ID 713625, 2010. · Zbl 1193.47054
[3] H. Bi and Y. Xing, “Poincaré-type inequalities with Lp(log L)\alpha -norms for Green’s operator,” Computers and Mathematics with Applications, vol. 60, no. 10, pp. 2764-2770, 2010. · Zbl 1207.58022
[4] B. Liu, “Ar\lambda (\Omega )-weighted imbedding inequalities for A-harmonic tensors,” Journal of Mathematical Analysis and Applications, vol. 273, no. 2, pp. 667-676, 2002. · Zbl 1035.46024
[5] Y. Wang, “Two-weight Poincaré-type inequalities for differential forms in Ls(\mu )-averaging domains,” Applied Mathematics Letters, vol. 20, no. 11, pp. 1161-1166, 2007. · Zbl 1144.58003
[6] X. Yuming, “Weighted integral inequalities for solutions of the A-harmonic equation,” Journal of Mathematical Analysis and Applications, vol. 279, no. 1, pp. 350-363, 2003. · Zbl 1021.31004
[7] Y. Xing and Y. Wang, “Bmo and Lipschitz norm estimates for composite operators,” Potential Analysis, vol. 31, no. 4, pp. 335-344, 2009. · Zbl 1179.26044
[8] Y. Xing, “A new weight class and Poincaré inequalities with the Radon measures,” Journal of Inequalities and Applications, vol. 2012, article 32, 2012. · Zbl 1279.26038
[9] S. M. Buckley and P. Koskela, “Orlicz-hardy inequalities,” Illinois Journal of Mathematics, vol. 48, no. 3, pp. 787-802, 2004. · Zbl 1070.46018
[10] S. G. Staples, “Lp-averaging domains and the Poincaré inequality,” Annales Academiæ Scientiarum Fennicæ Mathematica, vol. 14, pp. 103-127, 1989. · Zbl 0706.26010
[11] S. Ding and C. A. Nolder, “Ls(\mu )-averaging domains,” Journal of Mathematical Analysis and Applications, vol. 283, no. 1, pp. 85-99, 2003. · Zbl 1027.30053
[12] S. Ding, “L\varphi (\mu )-averaging domains and the quasi-hyperbolic metric,” Computers and Mathematics with Applications, vol. 47, no. 10-11, pp. 1611-1618, 2004. · Zbl 1063.30022
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