Liouville theorem for Dunkl polyharmonic functions.
Decomposition of polyharmonic functions with respect to the complex Dunkl Laplacian.
Harmonic Bergman spaces with small exponents in the unit ball.
Almansi decompositions for polyharmonic, polyheat, and polywave functions
We construct Almansi decompositions for a class of differential operators, which include powers of the classical Laplace operator, heat operator, and wave operator. The decomposition is given in a constructive way.
The diagonal mapping in mixed norm spaces
For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space of the polydisc onto the mixed norm space of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.
Radial derivative on bounded symmetric domains
We establish weighted Hardy-Littlewood inequalities for radial derivative and fractional radial derivatives on bounded symmetric domains.
Hölder functions in Bergman type spaces
It seems impossible to extend the boundary value theory of Hardy spaces to Bergman spaces since there is no boundary value for a function in a Bergman space in general. In this article we provide a new idea to show what is the correct version of Bergman spaces by demonstrating the extension to Bergman spaces of a result of Hardy-Littlewood in Hardy spaces, which characterizes the Hölder class of boundary values for a function from Hardy spaces in the unit disc in terms of the growth of its derivative....
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