Factorization and extrapolation of pairs of weights
Factorization theorem for product Hardy spaces
We extend the well known factorization theorems on the unit disk to product Hardy spaces, which generalizes the previous results obtained by Coifman, Rochberg and Weiss. The basic tools are the boundedness of a certain bilinear form on ℝ²₊ × ℝ²₊ and the characterization of BMO(ℝ²₊ × ℝ²₊) recently obtained by Ferguson, Lacey and Sadosky.
Fixed points of the Hardy-Littlewood maximal operator.
Fluides légèrement compressibles et limite incompressible
Fourier analysis in several parameters.
Clearly, one of the most basic contributions to the fields of real variables, partial differential equations and Fourier analysis in recent times has been the celebrated theorem of Calderón and Zygmund on the boundedness of singular integrals on Rn [1].
Fourier series and the maximal operator on the weighted special atom spaces.
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 integrals on spaces of homogeneous type
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.
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.