Fourier coefficients and growth of harmonic functions.
Fourier problem with bounded Baire data
The Fourier problem on planar domains with time moving boundary is considered using integral equations. Solvability of those integral equations in the space of bounded Baire functions as well as the convergence of the corresponding Neumann series are proved.
Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Part I: Schrödinger Equations.
Fractal Differential Equations on the Sierpinski Gasket.
Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes
Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.Wentzell boundary value problem for pseudo-differential operators generating Markov processes but not satisfying the transmission condition are not well understood. Studying fractional derivatives and fractional powers of such operators gives some insights in this problem. Since an L^p – theory for such operators will provide a helpful tool we investigate the L^p –domains of certain model operators.* This work is partially supported...
Fractional derivatives, non-symmetric and time-dependent Dirichlet forms and the drift form.
Fractional Hardy inequality with a remainder term
We prove a Hardy inequality for the fractional Laplacian on the interval with the optimal constant and additional lower order term. As a consequence, we also obtain a fractional Hardy inequality with the best constant and an extra lower order term for general domains, following the method of M. Loss and C. Sloane [J. Funct. Anal. 259 (2010)].
Fractional Hardy-Sobolev-Maz'ya inequality for domains
We prove a fractional version of the Hardy-Sobolev-Maz’ya inequality for arbitrary domains and norms with p ≥ 2. This inequality combines the fractional Sobolev and the fractional Hardy inequality into a single inequality, while keeping the sharp constant in the Hardy inequality.
Fractional integration on Hardy spaces
Fractional integro-differentiation in harmonic mixed norm spaces on a half-space
In this paper some embedding theorems related to fractional integration and differentiation in harmonic mixed norm spaces on the half-space are established. We prove that mixed norm is equivalent to a “fractional derivative norm” and that harmonic conjugation is bounded in for the range , . As an application of the above, we give a characterization of by means of an integral representation with the use of Besov spaces.
Fredholm radius of a potential theoretic operator for convex sets
Fredholm spectrum and Grunsky inequalities in general domains
Free boundary regularity for harmonic measures and Poisson kernels.
From Attraction Theory to Existence Proofs: The Evolution of Potential-Theoretic Methods in the Study of Boundary-Value Problems, 1860–1890
This paper examines developments in the study of boundary-value problems between about 1860 and 1890, in the context of the general evolution of this theory from the physical models in which the subject has its roots to a free-standing part of pure mathematics. The physically-motivated work of Carl Neumann and his method of the arithmetic mean appear as an initial phase in this development, one which employs physical models as an integral part of its reasoning and which concentrates on geometrical...
Full-Hyperharmonic Structures on Harmonic Spaces. II.
Full-Hyperharmonic Structures on Harmonie Spaces. I.
Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces [Book]
Functional approach to the Brelot-Keldych theorem
Functional inequalities and manifolds with nonnegative weighted Ricci curvature
We show that -dimensional complete and noncompact metric measure spaces with nonnegative weighted Ricci curvature in which some Caffarelli-Kohn-Nirenberg type inequality holds are isometric to the model metric measure -space (i.e. the Euclidean metric -space). We also show that the Euclidean metric spaces are the only complete and noncompact metric measure spaces of nonnegative weighted Ricci curvature satisfying some prescribed Sobolev type inequality.
Functions continuous in the fine topology for the heat equation