相关论文: BMOA estimates and radial growth of $B_{\phi}$ fun…
We characterize the restrictions of B\'ekoll\'e--Bonami weights of bounded hyperbolic oscillation, to subsets of the unit disc, thus proving an analogue of Wolff's restriction theorem for Muckenhoupt weights. Sundberg proved a discrete…
We provide variational estimates for Bloch functions on the unit ball of $\mathbb{R}^d$ extending previous work on the Anderson conjecture for conformal maps on the unit disc.
We study radial behavior of harmonic functions in the unit disk belonging to the Korenblum class. We prove that functions which admit two-sided Korenblum estimate either oscillate or have slow growth along almost all radii.
In this paper, the authors first consider the bidirectional estimates of several typical integrals. As some applications of these integral estimates, the authors investigate the pointwise multipliers from the normal weight general function…
In this article, we study the multi-dimensional Bohr radii of holomorphic functions defined on the Banach sequence spaces with values in the Banach spaces. For the case of finite dimensional Banach spaces, we exhibit the exact asymptotic…
The Bergman projection $P_\alpha$, induced by a standard radial weight, is bounded and onto from $L^\infty$ to the Bloch space $\mathcal{B}$. However, $P_\alpha: L^\infty\to \mathcal{B}$ is not a projection. This fact can be emended via the…
In this paper, we study a more general version of multidimensional Bohr radii for the holomorphic functions defined on unit ball of $\ell^n_q\,\,(1\leq q\leq \infty)$ spaces with values in arbitrary complex Banach spaces. More precisely, we…
We study radial behavior of analytic and harmonic functions, which admit a certain majorant in the unit disk. We prove that extremal growth or decay may occur only along small sets of radii and give precise estimates of these exceptional…
This paper studies functions of bounded mean oscillation (BMO) on metric spaces equipped with a doubling measure. The main result gives characterizations for mappings that preserve BMO. This extends the corresponding Euclidean results by…
For normalised analytic functions $f$ defined on the open unit disc $\mathbb{D}$ satisfying the condition $\sup_{z\in \mathbb{D}}(1-|z^2|) |f'(z)|\leq 1$, known as Bloch functions, we determine various starlikeness radii.
The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch…
In the paper "Bellman function for extremal problems in $\mathrm{BMO}$", the authors built the Bellman function for integral functionals on the $\mathrm{BMO}$ space. The present paper provides a development of the subject. We abandon the…
For the classical space of functions with bounded mean oscillation, it is well known that VMO** = BMO and there are many characterizations of the distance from a function f in BMO to VMO. When considering the Bloch space, results in the…
We present a unified method to obtain weighted estimates of linear and multilinear commutators with BMO functions, that is amenable to a plethora of operators and functional settings. Our approach elaborates on a commonly used Cauchy…
In this paper we prove sharp weighted BMO estimates for singular integrals, and we show how such estimates can be extrapolated to Banach function spaces.
The main aim of this paper is to study multidimensional Bohr radii for holomorphic functions defined in complete Reinhardt domains in $\mathbb{C}^n$ with values in complex Banach spaces. More specifically, for holomorphic functions with…
We study analogues of well-known relationships between Muckenhoupt weights and $BMO$ in the setting of Bekoll\'e-Bonami weights. For Bekoll\'e-Bonami weights of bounded hyperbolic oscillation, we provide distance formulas of Garnett and…
We consider a Riesz $\phi$-variation for functions $f$ defined on the real line when $\varphi:\Omega\times[0,\infty)\to[0,\infty)$ is a generalized $\Phi$-function. We show that it generates a quasi-Banach space and derive an explicit…
The concept of the Bohr radius of a pair of Banach spaces is introduced. The lower estimate for the value of the Bohr radius from the Bloch space to the space of bounded functions obtained by I. Kayumov, S. Ponnusamy and N. Shakirov is…
Recently, Kayumov \cite{K} obtained a sharp estimate for the $n$-th truncated area functional for normalized functions in the Bloch space for $n\le 5$ and then, together with Wirths \cite{KW1}, extended the result for $n=6$. We prove that…