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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.

##### MSC:
 42B25 Maximal functions, Littlewood-Paley theory
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##### 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 New York · Zbl 0373.53001 [3] Westenholz, C., Differential forms in mathematical physics, (1978), North Holland Publishing Amesterdam · Zbl 0391.58001 [4] Warner, F.W., Foundations of differentiable manifolds and Lie groups, (1983), 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 [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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