arXiv subjects

Taneli Korhonen

Publications and source records attributed to Taneli Korhonen.

4 recordsLinked to original sources

arXiv2019

Two-Weight Tb Theorems for Well-Localized Operators

This paper first defines operators that are "well-localized" with respect to a pair of accretive functions and establishes a global two-weight Tb theorem for such operators. Then it defines operators that are "well-localized" with respect to a pair of accretive systems and establishes a local two-weight Tb theorem for them. The proofs combine recent Tb proof techniques with arguments used to prove earlier T1 theorems for well-localized operators.

math.CA↗

arXiv2018

Radial averaging operator acting on Bergman and Lebesgue spaces

It is shown that the radial averaging operator $$ T_ω(f)(z)=\frac{\int_{|z|}^1f\left(s\frac{z}{|z|}\right)ω(s)\,ds}{\widehatω(z)},\quad \widehatω(z)=\int_{|z|}^1ω(s)\,ds, $$ induced by a radial weight $ω$ on the unit disc $\mathbb{D}$, is bounded from the weighted Bergman space $A^p_ν$, where $0 0, $$ are established for arbitrary radial weights $ω$, $ν$ and $η$. Moreover, differences and interrelationships between the cases $A^p_ν\to L^p_ν$, $L^p_ν\to L^p_ν$ and $L^p_ν\to L^{p,\infty}_ν$ are analyzed.

math.CV↗

arXiv2018

Radial two weight inequality for maximal Bergman projection induced by a regular weight

It is shown in quantitative terms that the maximal Bergman projection \begin{equation*} P^{+}_ω(f)(z)=\int_\mathbb{D} f(ζ)|B^ω_z(ζ)|ω(ζ)\,dA(ζ), \end{equation*} is bounded from $L^p_ν$ to $L^p_η$ if and only if \begin{equation*} \sup_{0<r<1}\left(\int_0^r\frac{η(s)}{\left(\int_{s}^1ω(t)\,dt\right)^p}\,ds\right)^{\frac{1}{p}} \left(\int_r^1\left(\frac{ω(s)}{ν(s)^\frac{1}{p}}\right)^{p'}ds\right)^{\frac{1}{p'}}<\infty, \end{equation*} provided $ω,ν,η$ are radial regular weights. A radial weight $σ$ is regular if it satisfies $σ(r)\asymp\int_{r}^1σ(t)\,dt/(1-r)$ for all $0\leq r<1$. It is also shown that under an appropriate additional hypothesis involving $ω$ and $η$, the Bergman projection $P_ω$ and $P^+_ω$ are simultaneously bounded.

math.CV↗

arXiv2017

Zero sequences, factorization and sampling measures for weighted Bergman spaces

The zero sets of the Bergman space $A^p_ω$ induced by either a radial weight $ω$ admitting a certain doubling property or a non-radial Bekollé-Bonami type weight are characterized in the spirit of Luecking's results from 1996. Accurate results obtained en route to this characterization are used to generalize Horowitz's factorization result from 1977 for functions in $A^p_ω$. The utility of the obtained factorization is illustrated by applications to integration and composition operators as well as to small Hankel operator induced by a conjugate analytic symbol. Dominating sets and sampling measures for the weighted Bergman space $A^p_ω$ induced by a doubling weight are also studied. Several open problems related to the scheme of the paper are posed.

math.CV↗