Norm comparison theorems

  • Ravi P. AgarwalEmail author
  • Shusen Ding
  • Craig Nolder


In the previous chapter, we have discussed various versions of the Hardy–Littlewood inequality for a pair of solutions u and v of the conjugate A-harmonic equation. The purpose of this chapter is to present some norm comparison inequalities for differential forms satisfying the conjugate A-harmonic equations, which have been recently established in [104]. Since the proofs display a general method to obtain L p -estimates, we include most of them in this chapter. Also, we always assume that 1 < p < ∞ and p −1 + q −1 = 1 throughout this chapter.


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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA
  2. 2.Department of MathematicsSeattle UniversitySeattleUSA
  3. 3.Department of MathematicsFlorida State UniversityTallahasseeUSA

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