Fourier series and the maximal operator on the weighted special atom spaces.
Fourier transform, restriction theorem, and scaling
In questo lavoro facciamo vedere, con un argomento di omogeneità di tipo Knapp, che se vale un teorema di restrizione per una ipersuperficie compatta, convessa e di tipo finito, allora si possono provare stime isotropiche ottimali per la trasformata di Fourier della misura di indotta dalla misura di Lebesgue sulla superficie.
Fourier transform of characteristic functions and Lebesgue constants for multiple Fourier series
Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces
Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Part II: The KDV Equation.
Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Part I: Schrödinger Equations.
Fourier transforms of Lipschitz functions on the hyperbolic plane .
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.
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 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 integrals on spaces of homogeneous type
Fractional integration on Hardy spaces
Fractional integration on the space and its dual
Fractional Maximal Functions in Metric Measure Spaces
We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.
Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces
In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels [...] TΩ,αA1,A2,…,Ak, which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces Mp,ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with w ∈ Ap,q which ensures the boundedness of the operators [...] TΩ,αA1,A2,…,Ak, from [...] Mp,φ1wptoMp,φ2wq for 1 < p < q < ∞. In all cases the conditions for...
Frames associated with expansive matrix dilations.
We construct wavelet-type frames associated with the expansive matrix dilation on the Anisotropic Triebel-Lizorkin spaces. We also show the a.e. convergence of the frame expansion which includes multi-wavelet expansion as a special case.
Function spaces on the snowflake
We consider two types of Besov spaces on the closed snowflake, defined by traces and with the help of the homeomorphic map from the interval [0,3]. We compare these spaces and characterize them in terms of Daubechies wavelets.
Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces [Book]
Functions which are Fourier transforms of distributions