Fourier -transform of distributions
Fourier series and Hilbert transforms with values in UMD Banach spaces
Fourier series and the Colombeau algebra on the unit circle
Fourier transform and distributional representation of the gamma function leading to some new identities.
Fourier transforms in generalized Fock spaces.
Fourier transforms of convolution operators
Fourier transforms of homogeneous distribution
Fourier Transforms of Lipschitz Functions and Fourier Multipliers on Compact Groups.
Fourier--Rademacher coefficients of functions in rearrangement-invariant spaces.
Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group
The sub-Laplacian on the Heisenberg group is first decomposed into twisted Laplacians parametrized by Planck's constant. Using Fourier-Wigner transforms so parametrized, we prove that the twisted Laplacians are globally hypoelliptic in the setting of tempered distributions. This result on global hypoellipticity is then used to obtain Liouville's theorems for harmonic functions for the sub-Laplacian on the Heisenberg group.
Fractal functions and Schauder bases
Fractals, trees and the Neumann Laplacian.
Fractional Derivatives in Spaces of Generalized Functions
MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of distributions.
Fractional Hajłasz-Morrey-Sobolev spaces on quasi-metric measure spaces
In this article, via fractional Hajłasz gradients, the authors introduce a class of fractional Hajłasz-Morrey-Sobolev spaces, and investigate the relations among these spaces, (grand) Morrey-Triebel-Lizorkin spaces and Triebel-Lizorkin-type spaces on both Euclidean spaces and RD-spaces.
Fractional Hardy inequalities and visibility of the boundary
We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection with the boundedness of extension operators for fractional Sobolev spaces.
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 integral operators on with Morrey-Campanato norms
We introduce function spaces with Morrey-Campanato norms, which unify , and Morrey-Campanato spaces, and prove the boundedness of the fractional integral operator on these spaces.
Fractional integration on Hardy spaces
Fractional integration on the space and its dual