Painlevé' s Theorem and the Phragmén-Lindelöf Maximum Principle.
Parabolic Harnack inequality and local limit theorem for percolation clusters.
Parabolic measure on domains of class Lip
Parabolic potentials and wavelet transforms with the generalized translation
Parabolic wavelet transforms associated with the singular heat operators and , where , are introduced. These transforms are defined in terms of the relevant generalized translation operator. An analogue of the Calderón reproducing formula is established. New inversion formulas are obtained for generalized parabolic potentials representing negative powers of the singular heat operators.
Parapolicity and existence of bounded biharmonic functions
Permanent sets of measures charging no exceptional sets and the Feynman-Kac Formula.
Perron-Frobenius operators and the Klein-Gordon equation
For a smooth curve and a set in the plane , let be the space of finite Borel measures in the plane supported on , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on . Following [12], we say that is a Heisenberg uniqueness pair if . In the context of a hyperbola , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the...
Perturbation of a biharmonic eigenvalue problem
Perturbation theory for nonlinear Dirichlet problems.
p-harmonic equation and quasiregular mappings
Pointwise and locally uniform convergence of holomorphic and harmonic functions.
Pointwise and locally uniform convergence of holomorphic and harmonic functions
We shall characterize the sets of locally uniform convergence of pointwise convergent sequences. Results obtained for sequences of holomorphic functions by Hartogs and Rosenthal in 1928 will be generalized for many other sheaves of functions. In particular, our Hartogs-Rosenthal type theorem holds for the sheaf of solutions to the second order elliptic PDE's as well as it has applications to the theory of harmonic spaces.
Pointwise inequalities and approximation in fractional Sobolev spaces
We prove that a function belonging to a fractional Sobolev space may be approximated in capacity and norm by smooth functions belonging to , 0 < m + λ < α. Our results generalize and extend those of [12], [4], [14], and [11].
Pointwise inequalities for Sobolev functions and some applications
We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer’s theorem which states that Sobolev functions can be approximated by functions both in norm and capacity.
Pointwise multiplicative inequalities and Nirenberg type estimates in weighted Sobolev spaces
Poisson Integrals and Boundary Components of Symmetric Spaces.
Poisson kernel characterization of Reifenberg flat chord arc domains
Positive Approximate Identities and Lattice-Ordered Dual spaces.
Positive Schatten class Toeplitz operators on the ball
On the harmonic Bergman space of the ball, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten class operator in terms of averaging functions and Berezin transforms.
Positive Toeplitz operators between the pluriharmonic Bergman spaces
We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space into another for in terms of certain Carleson and vanishing Carleson measures.