Biholomorphic invariance of capacity and the capacity of an annulus
Bivariate Revuz measures and the Feynman-Kac formula
BMO and Lipschitz approximation by solutions of elliptic equations
We consider the problem of qualitative approximation by solutions of a constant coefficients homogeneous elliptic equation in the Lipschitz and BMO norms. Our method of proof is well-known: we find a sufficient condition for the approximation reducing matters to a weak spectral synthesis problem in an appropriate Lizorkin-Triebel space. A couple of examples, evolving from one due to Hedberg, show that our conditions are sharp.
BMO estimates for biharmonic multiple layer potentials
BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev spaces.
The spectral synthesis theorem for Sobolev spaces of Hedberg and Wolff [7] has been applied in combination with duality, to problems of Lq approximation by analytic and harmonic functions. In fact, such applications were one of the main motivations to consider spectral synthesis problems in the Sobolev space setting. In this paper we go the opposite way in the context of the BMO-H1 duality: we prove a BMO approximation theorem by harmonic functions and then we apply the ideas in its proof to produce...
Böcher's theorem in a space of dimension one
Boundaries and the Fatou theorem for subelliptic second order operators on solvable Lie groups
Boundaries for left-invariant sub-elliptic operators on semidirect products of nilpotent and abelian groups.
Boundaries of graphs of harmonic functions.
Boundary behavior of subharmonic functions in nontangential accessible domains
The following results concerning boundary behavior of subharmonic functions in the unit ball of are generalized to nontangential accessible domains in the sense of Jerison and Kenig [7]: (i) The classical theorem of Littlewood on the radial limits. (ii) Ziomek’s theorem on the -nontangential limits. (iii) The localized version of the above two results and nontangential limits of Green potentials under a certain nontangential condition.
Boundary Behavior of Subharmonic Functions on the Unit Disk
Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains
Boundary behaviour of eigenfunctions of the Laplace operator on trees
Boundary behaviour of eigenfunctions of the Laplacian in a bi-tree.
Boundary behaviour of harmonic functions in a half-space and brownian motion
Let be harmonic in the half-space , . We show that can have a fine limit at almost every point of the unit cubs in but fail to have a nontangential limit at any point of the cube. The method is probabilistic and utilizes the equivalence between conditional Brownian motion limits and fine limits at the boundary.In it is known that the Hardy classes , , may be described in terms of the integrability of the nontangential maximal function, or, alternatively, in terms of the integrability...
Boundary behaviour of positive harmonic functions on Lipschitz domains.
Boundary estimates for derivatives of harmonic functions
Boundary Harnack principle for separated semihyperbolic repellers, harmonic measure applications.
Boundary integral equations of plane elasticity in domains with peaks.
Boundary integral methods for harmonic differential forms in Lipschitz domains.