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Poincaré‐Type Inequalities for the Composite Operator in L𝒜‐Averaging Domains

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Listed:
  • Guannan Shi
  • Yuming Xing
  • Baiqing Sun

Abstract

We first establish the local Poincaré inequality with L𝒜‐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 L𝒜‐averaging domains and relative properties, we demonstrate the global Poincaré inequality with L𝒜‐averaging domains. Finally, we give some illustrations for these theorems.

Suggested Citation

  • Guannan Shi & Yuming Xing & Baiqing Sun, 2014. "Poincaré‐Type Inequalities for the Composite Operator in L𝒜‐Averaging Domains," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:675464
    DOI: 10.1155/2014/675464
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    References listed on IDEAS

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    1. Casey Johnson & Shusen Ding, 2013. "Integral Estimates for the Potential Operator on Differential Forms," International Journal of Analysis, Hindawi, vol. 2013, pages 1-6, January.
    2. Ravi P. Agarwal & Shusen Ding & Craig Nolder, 2009. "Inequalities for Differential Forms," Springer Books, Springer, number 978-0-387-68417-8, March.
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