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Almansi decompositions for polyharmonic, polyheat, and polywave functions

100%
Ren G., Kähler U.
Studia Mathematica
|
2006
|
tom 172
|
nr 1
91-100
EN
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.
2
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Radial derivative on bounded symmetric domains

100%
Ren G., Kähler U.
Studia Mathematica
|
2003
|
tom 157
|
nr 1
57-70
EN
We establish weighted Hardy-Littlewood inequalities for radial derivative and fractional radial derivatives on bounded symmetric domains.
3
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Hölder functions in Bergman type spaces

100%
Chen Y., Ren G.
Studia Mathematica
|
2012
|
tom 212
|
nr 3
237-258
EN
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. To this end, a class of Hölder functions in Bergman spaces is introduced in terms of the modulus of continuity and we establish its characterization in terms of radial derivatives. The classical result of Hardy-Littlewood in the Hardy space can be thought of as the limit case, matching the fact that the Hardy space is a limit of Bergman spaces.
4
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The diagonal mapping in mixed norm spaces

100%
Ren G., Shi J.
Studia Mathematica
|
2004
|
tom 163
|
nr 2
103-117
EN
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 𝓓F(z) = F(z,...,z), and prove that the diagonal mapping 𝓓 maps the mixed norm space $H^{p,q,α}(Uⁿ)$ of the polydisc onto the mixed norm space $H^{p,q,|α|+(p/q+1)(n-1)}(U)$ of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.
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