相关论文: Extremal problems in BMO and VMO involving the Gar…

Let (M,\mu) be a sigma-finite measure space. Let (T_t) be a semigroup of positive preserving maps on (M,\mu) with standard assumptions. We prove a H_1-BMO duality theory with assumptions only on T_t. The BMO is defined as spaces of…

Let $X$ be a metric space with doubling measure, and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ whose heat kernel satisfies the Gaussian upper bound. Let $f$ be in the space $ {\rm BMO}_L(X)$ associated with the operator $L$ and…

We consider maximal kernel-operators on abstract measure spaces $(X,\mu)$ equipped with a ball-basis. We prove that under certain asymptotic condition on the kernels those operators maps boundedly BMO(X) into BLO(X), generalizing the…

On spaces of finite signed Borel measures on a metric space one has introduced the Fortet-Mourier and Dudley norms, by embedding the measures into the dual space of the Banach space of bounded Lipschitz functions, equipped with different --…

We prove that every measurable function $f:\,[0,a]\to\mathbb{C}$ such that $|f|=1$ a.e. on $[0,a]$ is an extreme point of the unit ball of the Lorentz space $\Lambda(\varphi)$ on $[0,a]$ whenever $\varphi$ is a not linear, strictly…

We prove that for any homogeneous, second order, constant complex coefficient elliptic system $L$, the Dirichlet problem in $\mathbb{R}^{n}_{+}$ with boundary data in BMO is well-posed in the class of functions $u$ with…

Given a Banach space $\mathcal X$, let $x$ be a point in $\text{ball}(\mathcal X)$, the closed unit ball of $\mathcal X$. One says that $x$ is a strongly extreme point of $\text{ball}(\mathcal X)$ if it has the following property: for every…

We study the BMO-type functional $\kappa_{\varepsilon}(f,\mathbb R^n)$, which can be used to characterize BV functions $f\in BV(\mathbb R^n)$. The $\Gamma$-limit of this functional, taken with respect to $L^1_{\mathrm{loc}}$-convergence, is…

For a bounded function $\varphi$ on the unit circle $\mathbb T$, let $T_\varphi$ be the associated Toeplitz operator on the Hardy space $H^2$. Assume that the kernel $$K_2(\varphi):=\{f\in H^2:\,T_\varphi f=0\}$$ is nontrivial. Given a…

By $BMO_o(R)$ we denote the space consisting of all those odd and bounded mean oscillation functions on R. In this paper we characterize the functions in $BMO_o(R)$ with bounded support as those ones that can be written as a sum of a…

Given a subset $\Lambda$ of $\mathbb Z_+:=\{0,1,2,\dots\}$, let $H^\infty(\Lambda)$ denote the space of bounded analytic functions $f$ on the unit disk whose coefficients $\widehat f(k)$ vanish for $k\notin\Lambda$. Assuming that either…

We introduce the notion of numerical (strong) peak function and investigate the denseness of the norm and numerical peak functions on complex Banach spaces. Let $A_b(B_X:X)$ be the Banach space of all bounded continuous functions $f$ on the…

This paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let $dA$ and $dm$ denote Lebesgue measures on the unit disc $D$ and the unit circle $\mathbb T$, respectively. For…

We consider the space $A(\mathbb{T}^d)$ of absolutely convergent Fourier series on the torus $\mathbb{T}^d$. The norm on $A(\mathbb{T}^d)$ is naturally defined by $\|f\|_{A}=\|\widehat{f}\|_{l^1}$, where $\widehat{f}$ is the Fourier…

Analytic functions in the Hardy class $H^2$ over the upper half-plane $\mathbb{H}_+$ are uniquely determined by their values on any curve $\Gamma$ lying in the interior or on the boundary of $\mathbb{H}_+$. The goal of this paper is to…

Let $L$ be a second order elliptic operator on $R^d$ with a constant diffusion matrix and a dissipative (in a weak sense) drift $b \in L^p_{loc}$ with some $p>d$. We assume that $L$ possesses a Lyapunov function, but no local boundedness of…

In this paper we calculate the norm of the generalized maximal operator $M_{\phi,\Lambda^{\alpha}(b)}$, defined with $0 < \alpha < \infty$ and functions $b,\,\phi: (0,\infty) \rightarrow (0,\infty)$ for all measurable functions $f$ on…

We characterize the algebra $H^\infty \circ L_{m}$, where $m$ is a point of the maximal ideal space of $H^\infty$ with nontrivial Gleason part $P(m)$ and $L_{m} : \mathbb{D}\to P(m)$ is the coordinate Hoffman map. In particular, it is shown…

We are concerned with extensions of the Mason--Stothers $abc$ theorem from polynomials to analytic functions on the unit disk $\mathbb D$. The new feature is that the number of zeros of a function $f$ in $\mathbb D$ gets replaced by the…

We prove a Lusin approximation of functions of bounded variation. If $f$ is a function of bounded variation on an open set $\Omega\subset X$, where $X=(X,d,\mu)$ is a given complete doubling metric measure space supporting a $1$-Poincar\'e…