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Ling, Yi; Gejun, Bao

Some local Poincaré inequalities for the composition of the sharp maximal operator and the Green’s operator. (English) Zbl 1238.42006

Comput. Math. Appl. 63, No. 3, 720-727 (2012).
Summary: We establish the local Poincaré-type inequalities for the composition of the sharp maximal operator and the Green’s operator with an Orlicz norm.

Cited in 6 Documents

MSC:

42B25 Maximal functions, Littlewood-Paley theory

Keywords:

Poincaré-type inequalities; Orlicz norm; the sharp maximal operator and the Green’s operator
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\textit{Y. Ling} and \textit{B. Gejun}, Comput. Math. Appl. 63, No. 3, 720--727 (2012; Zbl 1238.42006)
Full Text: DOI

References:

[1] Agarwal, R. P.; Ding, S.; Nolder, C. A., Inequalities for Differential Forms (2009), Springer · Zbl 1184.53001
[2] Sachs, S. K.; Wu, H., General Relativity for Mathematicians (1977), Springer: Springer New York · Zbl 0373.53001
[3] Westenholz, C., Differential Forms in Mathematical Physics (1978), North Holland Publishing: North Holland Publishing Amesterdam · Zbl 0391.58001
[4] Warner, F. W., Foundations of Differentiable Manifolds and Lie Groups (1983), Springer-Verlag: Springer-Verlag New York · Zbl 0516.58001
[5] Ling, Yi; Umoh, Hanson M., Global estimates for singular integrals of the composition of the maximal operator and the Green’s operator, J. Inequal. Appl., 2010 (2010), Article ID 723234 · Zbl 1201.42014
[6] Ding, S., Norm estimate for the maximal operator and Green’s operator, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 16, 72-78 (2009), Differ. Equ. Dyn. Syst., (suppl. S1) · Zbl 1182.47018
[7] Ding, S., \(L^\varphi(\mu)\)-averaging domains and the quasihyperbolic metric, Comput. Math. Appl., 47, 1611-1618 (2004) · Zbl 1063.30022
[8] Nolder, C. A., Global integrability theorem for \(A\)-harmonic tensors, J. Math. Anal. Appl., 247, 236-245 (2000) · Zbl 0973.35074
[9] Stein, E. M., Harmonic Analysis (1993), Princeton University Press: Princeton University Press Princeton
[10] Buckley, S. M.; Koskela, P., Orlicz-Hardy inequaties, Illinois J. Math., 48, 787-802 (2004) · Zbl 1070.46018
[11] Ding, S., \(L(\varphi, \mu)\)-averaging domains and Poincaré inequalities with Orlicz norm, Nonlinear Anal., 73, 256-265 (2010) · Zbl 1202.46033
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