Abstract
In this article, we first prove Orlicz norm inequalities for the composition of the homotopy operator and the projection operator acting on solutions of the nonhomogeneous A-harmonic equation. Then we develop these estimates to Lφ(µ)-averaging domains. Finally, we give some specific examples of Young functions and apply them to the norm inequality for the composite operator.2000 Mathematics Subject Classification: Primary 26B10; Secondary 30C65, 31B10, 46E35.
Highlights
Differential forms as the extensions of functions have been rapidly developed
Some important results have been widely used in PDEs, potential theory, nonlinear elasticity theory, and so forth; see [1,2,3,4,5,6,7] for details
The study on operator theory of differential forms just began in these several years and attracts the attention of many people
Summary
Differential forms as the extensions of functions have been rapidly developed. In recent years, some important results have been widely used in PDEs, potential theory, nonlinear elasticity theory, and so forth; see [1,2,3,4,5,6,7] for details. The definition of the homotopy operator for differential forms was first introduced in [9]. Let u ∈ Lsloc(D, ∧k), k = 1, 2,..., n, 1 < s 0 a.e. and sup. We need the following reverse Hölder inequality for the solutions of the nonhomogeneous A-harmonic equation, which appears in [3]. Assume that u is a smooth solution of the nonhomogeneous A-harmonic equation in a bounded convex domain.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
