Related papers: Endpoint Estimates for N-dimensional Hardy Operato…
Our aim is to characterize the Lipschitz functions by variable exponent Lebesgue spaces. We give some characterizations of the boundedness of the maximal or nonlinear commutators of the Hardy-Littlewood maximal function and sharp maximal…
Via the new weight function $A_{\vec p}^{\theta }(\varphi )$, the authors introduce a new class of multilinear Littlewood--Paley $g_{\lambda}^{*}$ functions and establish the boundedness on weighted Lebesgue spaces. In addition, the authors…
Characterizations of the associated spaces and second associated spaces of the Hardy space on $\mathbb{R}^n$ are given. Some results on the associated spaces of the $\textrm{BMO}(\mathbb{R}^n)$ space are proved also.
The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space $%H_{p}$ to the Lebesgue…
In this paper the boundedness of the weighted iterated Hardy-type operators $T_{u,b}$ and $T_{u,b}^*$ involving suprema from weighted Lebesgue space $L_p(v)$ into weighted Ces\`{a}ro function spaces ${\operatorname{Ces}}_{q}(w,a)$ are…
We obtain sufficient and necessary conditions on weight functions $s_1(t),\ldots,s_m(t)$ and $\psi(t)$ so that the weighted multilinear Hardy-Ces\`{a}ro operator \[(f_1,\ldots,f_m)\mapsto \int_{[0,1]^n}\left(\prod_{k=1}^nf_k\left(s_k(t)…
We obtain in this short article the non-asymptotic exact estimations for the norm of (generalized) weighted Hardy-Littlewood average integral operator in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the…
We show that the Hardy-Littlewood maximal operator is bounded on a reflexive variable Lebesgue space $L^{p(\cdot)}$ over a space of homogeneous type $(X,d,\mu)$ if and only if it is bounded on its dual space $L^{p'(\cdot)}$, where…
We obtain in this short article the non-asymptotic estimations for the norm of (generalized) Cesaro-Hardy integral operators in the so-called Bilateral Grand Lebesgue Spaces. We also give examples to show the sharpness of these…
We show that if an operator T is bounded on weighted Lebesgue space L^2(w) and obeys a linear bound with respect to the A_2 constant of the weight, then its commutator [b,T] with a function b in BMO will obey a quadratic bound with respect…
In this paper we study a variant of the uncentred Hardy--Littlewood maximal operator on Damek--Ricci spaces in which balls are replaced by suitable half balls. Perhaps surprisingly, such modified maximal operator has better boundedness…
In this paper we investigate the boundedness of classical operators, namely the Hardy-Littlewood maximal operator, fractional integral operators, and Calderon-Zygmund operators, on generalized weighted Morrey spaces and generalized weighted…
We study the boundedness of commutators of the Hardy-Littlewood maximal function and the sharp maximal function on weighted Morrey spaces when the symbols of the commutators belong to weighted Lipschitz spaces. Some new characterizations…
In this paper, the fractional Hardy-type operator of variable order $\beta(x)$ is shown to be bounded from the variable exponent Herz-Morrey spaces $M\dot{K}_{p_{_{1}},q_{_{1}}(\cdot)}^{\alpha(\cdot),\lambda}(\R^{n})$ into the weighted…
We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…
We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^\infty$…
We study two classes of bounded operators on mixed norm Lebesgue spaces, namely composition operators and product operators. A complete description of bounded composition operators on mixed norm Lebesgue spaces are given. For a certain…
In this paper, the boundedness properties of vector-valued intrinsic square functions and their vector-valued commutators with $BMO(\mathbb R^n)$ functions are discussed. We first show the weighted strong type and weak type estimates of…
This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more…
Let $(X,d,\mu)$ denotes non-homogeneous metric measure space satisfying geometrically doubling and the upper doubling measure condition. In this paper, the boundedness in Lebesgue spaces for two kinds of commutators, which are iterated…