A singular integral of the composite operator. (English) Zbl 1173.58300

Ding, Shusen; Liu, Bing

Appl. Math. Lett. 22, No. 8, 1271-1275 (2009).

Summary: We establish the Poincaré-type inequalities for the composition of the homotopy operator and the projection operator. We also obtain some estimates for the integral of the composite operator with a singular density.

MSC:

58A10

Differential forms in global analysis

Keywords:

Poincaré-type inequality; differential forms; \(A\)-harmonic equations; the homotopy operator and the projection operator

References:

[1]	Agarwal, R. P.; Ding, S., Advances in differential forms and the \(A\)-harmonic equations, Math. Comput. Modelling, 37, 1393-1426 (2003) · Zbl 1051.58001
[3]	Cartan, H., Differential Forms (1970), Houghton Mifflin Co.: Houghton Mifflin Co. Boston · Zbl 0213.37001
[4]	Iwaniec, T.; Lutoborski, A., Integral estimates for null Lagrangians, Arch. Ration. Mech. Anal., 125, 25-79 (1993) · Zbl 0793.58002
[5]	Scott, C., \(L^p\)-theory of differential forms on manifolds, Trans. Amer. Math. Soc., 347, 2075-2096 (1995) · Zbl 0849.58002
[6]	Ding, S., Two-weight Caccioppoli inequalities for solutions of nonhomogeneous \(A\)-harmonic equations on Riemannian manifolds, Proc. Amer. Math. Soc., 132, 2367-2375 (2004) · Zbl 1127.35021
[7]	Ding, S.; Nolder, C. A., \(L^s(\mu)\)-averaging domains, J. Math. Anal. Appl., 283, 85-99 (2003) · Zbl 1027.30053
[8]	Xing, Y., Weighted integral inequalities for solutions of the \(A\)-harmonic equation, J. Math. Anal. Appl., 279, 350-363 (2003) · Zbl 1021.31004
[9]	Xing, Y., Weighted Poincaré-type estimates for conjugate A-harmonic tensors, J. Inequal. Appl., 1, 1-6 (2005) · Zbl 1087.31009
[10]	Nolder, C., Global integrability theorems for \(A\)-harmonic tensors, J. Math. Anal. Appl., 247, 236-245 (2000) · Zbl 0973.35074