Radial limits of superharmonic functions in the plane
Radial limits of the Poisson kernel on the classical Cartan domains
Real analysis, quantitative topology, and geometric complexity.
In this paper, we give an overview of some topics involving behavior of homeomorphisms and ways in which real analysis can arise in geometric settings.
Rearrangement estimates of the area integrals
We derive weighted rearrangement estimates for a large class of area integrals. The main approach used earlier to study these questions is based on distribution function inequalities.
Rectilinearly and rectifiably ambiguous points of a function harmonic inside a sphere
Refinement of an Lp-Estimate of Solonnikov for a Parabolic Equation of the Second Order with Conormal Boundary Condition.
Regular growth of subharmonic functions of several variables.
Regularity of a free boundary with application to the Pompeiu problem.
Regularity of p-harmonic functions on the plane.
Regularizing sets of irregular points.
Relative Fatou theorem for harmonic functions of rotation invariant stable processes in smooth domains
For domains we give exact asymptotics near the domain’s boundary for the Green function and Martin kernel of the rotation invariant α-stable Lévy process. We also obtain a relative Fatou theorem for harmonic functions of the stable process.
Remarks on equilibrium potential and energy
This note discusses to problem of the minimization of energy by the equilibrium measure obtained by the method of last exit in reference Ann. Inst. Fourier, 23-3 (1973), 313–322.
Remarks on some fourth order variational inequalities
Remarks on subharmonic envelopes.
We prove that the subharmonic envelope of a lower semicontinuous function on Omega is harmonic on a certain open subset of Omega, using a very classical method in potential theory. The result gives simple proofs of theorems on harmonic measures and Jensen measures obtained by Cole and Ransford.
Remarks on the biharmonic Martin boundary and the integral representation of biharmonic functions. (Remarques sur la frontière de Martin biharmonique et la représentation intégrale des fonctions biharmoniques.)
Représentation intégrale des fonctions surharmoniques au moyen des réduites
Representation of Capacities.
Representation of multivariate functions via the potential theory and applications to inequalities.
Reproducing kernels for Dunkl polyharmonic polynomials
In this paper, we compute explicitly the reproducing kernel of the space of homogeneous polynomials of degree and Dunkl polyharmonic of degree , i.e. , , where is the Dunkl Laplacian and we study the convergence of the orthogonal series of Dunkl polyharmonic homogeneous polynomials.
Reproducing Kernels for Harmonic Bergman Spaces of the Unit Ball.