Abstract and Applied Analysis

Poincaré-Type Inequalities for the Composite Operator in L 𝒜 -Averaging Domains

Guannan Shi, Yuming Xing, and Baiqing Sun

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Abstract

We first establish the local Poincaré inequality with L 𝒜 -averaging domains for the composition of the sharp maximal operator and potential operator, applied to the nonhomogenous A -harmonic equation. Then, according to the definition of L 𝒜 -averaging domains and relative properties, we demonstrate the global Poincaré inequality with L 𝒜 -averaging domains. Finally, we give some illustrations for these theorems.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 675464, 7 pages.

Dates
First available in Project Euclid: 3 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412360600

Digital Object Identifier
doi:10.1155/2014/675464

Mathematical Reviews number (MathSciNet)
MR3176763

Citation

Shi, Guannan; Xing, Yuming; Sun, Baiqing. Poincaré-Type Inequalities for the Composite Operator in ${L}^{\mathrm{\scr A}}$ -Averaging Domains. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 675464, 7 pages. doi:10.1155/2014/675464. https://projecteuclid.org/euclid.aaa/1412360600


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