Related papers: Characterization of Lipschitz functions via commut…
Let $0<\alpha<n$ and $M_{\alpha}$ be the fractional maximal function. The nonlinear commutator of $M_{\alpha}$ and a locally integrable function $b$ is given by $[b,M_{\alpha}](f)=bM_{\alpha}(f)-M_{\alpha}(bf)$. In this paper, we mainly…
Let $0 \leq \alpha<n$ and $b$ be the locally integrable function. In this paper, we consider the maximal commutator of fractional maximal function $M_{b,\alpha}$ and the nonlinear commutator of fractional maximal function $[b, M_{\alpha}]$…
In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $M_{\alpha}$ on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator…
We give necessary and sufficient conditions for the boundedness of the maximal commutators $M_{b}$, the commutators of the maximal operator $[b, M]$ and the commutators of the sharp maximal operator $[b, M^{\sharp}]$ in Orlicz spaces…
Let $M$ be the Hardy-Littlewood maximal function and $b$ be a locally integrable function. Denote by $M_b$ and $[b,M]$ the maximal commutator and the (nonlinear) commutator of $M$ with $b$. In this paper, the author consider the boundedness…
In this paper, the main aim is to consider the boundedness of the fractional maximal commutator $M_{\alpha,b}$ and the nonlinear commutator $[b, M_{\alpha}]$ on the Lebesgue spaces over some stratified Lie group $\mathbb{G}$ when $b$…
In this paper, the main aim is to demonstrate the boundedness for commutators of (fractional) maximal function and sharp maximal function in the slice spaces, where the symbols of the commutators belong to the BMO space, whereby some new…
In this paper, the main aim is to consider the boundedness of commutators of multilinear Calder\'{o}n-Zygmund operators with Lipschitz functions in the context of the variable exponent Lebesgue spaces. Furthermore, the variable versions of…
We obtain some new characterizations of a variable version of Lipschitz spaces in terms of the boundedness of commutators of sharp maximal functions, fractional maximal functions or fractional maximal commutators in the context of the…
Let $M$ be the Hardy-Littlewood maximal function. Denote by $M_b$ and $[b,M]$ the maximal and the nonlinear commutators of $M$ with a function $b$. The boundedness of $M_b$ and $[b,M]$ on weighted Lebesgue spaces are characterized when the…
In this paper, the main aim is to consider the boundedness of the Hardy-Littlewood maximal commutator $M_{b}$ and the nonlinear commutator $[b, M]$ on the Lebesgue spaces and Morrey spaces over some stratified Lie group $\mathbb{G}$ when…
In this paper, the main aim is to consider the mapping properties of the maximal or nonlinear commutator for the fractional maximal operator with the symbols belong to the Lipschitz spaces on variable Lebesgue spaces in the context of…
Let $0<t<\infty$, $0<\alpha<n$, $1<p<r<\infty$ and $1<q<s<\infty$. In this paper, we prove that $b\in B M O\left(\mathbb{R}^{n}\right)$ if and only if the commutator $[b, T_{\Omega,\alpha}]$ generated by the fractional integral operator…
In this paper, the main aim is to give some characterizations of the boundedness of the maximal or nonlinear commutator of the $p$-adic fractional maximal operator $ \mathcal{M}_{\alpha}^{p}$ with the symbols belong to the $p$-adic…
In this paper, the sharp maximal theorem is generalized to mixed-norm ball Banach function spaces, which is defined as Definition 2.7. As an application, we give a characterization of BMO via the boundedness of commutators of fractional…
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…
Let $0<\alpha<n$ and $I_\alpha$ be the fractional integral operator. In this paper, we shall use a unified approach to show some boundedness properties of commutators $[b,I_\alpha]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under…
In this paper we give the complete characterization of the boundedness of the generalized fractional maximal operator $$ M_{\phi,\Lambda^{\alpha}(b)}f(x) : = \sup_{Q \ni x} \frac{\|f \chi_Q\|_{\Lambda^{\alpha}(b)}}{\phi (|Q|)} \qquad (x \in…
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 we prove necessary conditions for the boundedness of fractional operators on the variable Lebesgue spaces. More precisely, we find necessary conditions on an exponent function $\pp$ for a fractional maximal operator $M_\alpha$…