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

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.


42B25 Maximal functions, Littlewood-Paley theory
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.