Riesz conjugate functions theorem for harmonic quasiconformal mappings
Jinsong Liu, Jian‐Feng Zhu
Abstract
We generalize the Riesz conjugate functions theorem for planar harmonic K -quasiregular mappings (when 1 < p ≤ 2 ) and harmonic K -quasiconformal mappings (when 2 < p < ∞ ) in the unit disk. Moreover, if K = 1 , then our constant coincides with the classical analytic case. For the n dimensional case ( n > 2 ), we also obtain the Riesz conjugate functions theorem for invariant harmonic K -quasiregular mappings when 1 < p ≤ 2 .
Topics & Concepts
MathematicsConjugateHarmonic functionRiesz transformUnit diskInvariant (physics)Pure mathematicsM. Riesz extension theoremRiesz potentialMathematical analysisPlanarHarmonicRiesz representation theoremSubharmonic functionMathematical physicsComputer graphics (images)PhysicsComputer scienceQuantum mechanicsAnalytic and geometric function theoryDifferential Equations and Boundary ProblemsNonlinear Partial Differential Equations