arXiv subjects
Publications and source records attributed to Fatih Deringoz.
The main focus of this paper is commutators and maximal commutators on Orlicz spaces for fractional maximal functions and Riesz potential. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness in less restrictive terms.
In the present paper, we will characterize the boundedness of the generalized fractional integral operators $I_ρ$ and the generalized fractional maximal operators $M_ρ$ on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators $M_ρ$ and $I_ρ$ on generalized Orlicz--Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators $M_ρ$ and $I_ρ$ on generalized Orlicz--Morrey spaces.
In this paper, we investigate the boundedness of maximal operator and its commutators in generalized Orlicz-Morrey spaces on the spaces of homogeneous type. As an application of this boundedness, we give necessary and sufficient condition for the Adams type boundedness of fractional integral and its commutators in these spaces. We also discuss criteria for the boundedness of these operators in Orlicz spaces.
In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $M_α$ on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator $M_{b,α}$ and nonlinear commutator of fractional maximal operator $[b,M_α]$ on Orlicz spaces, when $b$ belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.
In the present paper, we shall give a characterization for weak/strong Adams-type boundedness of the fractional maximal operator on generalized Orlicz-Morrey spaces.
We consider generalized Orlicz-Morrey spaces $M_{Φ,φ}(\mathbb{R}^{n})$ including their weak versions $WM_{Φ,φ}(\mathbb{R}^{n})$. We find the sufficient conditions on the pairs $(φ_{1},φ_{2})$ and $(Φ, Ψ)$ which ensures the boundedness of the fractional maximal operator $M_α$ from $M_{Φ,φ_1}(\mathbb{R}^{n})$ to $M_{Ψ,φ_2}(\mathbb{R}^{n})$ and from $M_{Φ,φ_1}(\mathbb{R}^{n})$ to $WM_{Ψ,φ_2}(\mathbb{R}^{n})$. As applications of those results, the boundedness of the commutators of the fractional maximal operator $M_{b,α}$ with $b \in BMO(\mathbb{R}^{n})$ on the spaces $M_{Φ,φ}(\mathbb{R}^{n})$ is also obtained. In all the cases the conditions for the boundedness are given in terms of supremal-type inequalities on weights $φ(x,r)$, which do not assume any assumption on monotonicity of $φ(x,r)$ on $r$.
We consider generalized Orlicz-Morrey spaces $M_{Φ,φ}(\Rn)$ including their weak versions $WM_{Φ,φ}(\Rn)$. In these spaces we prove the boundedness of the Riesz potential from $M_{Φ,φ_1}(\Rn)$ to $M_{Ψ,φ_2}(\Rn)$ and from $M_{Φ,φ_1}(\Rn)$ to $WM_{Ψ,φ_2}(\Rn)$. As applications of those results, the boundedness of the commutators of the Riesz potential on generalized Orlicz-Morrey space is also obtained. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on $(φ_{1},φ_{2})$, which do not assume any assumption on monotonicity of $φ_{1}(x,r)$, $φ_{2}(x,r)$ in r.
We study the boundedness of intrinsic square functions and their commutators on generalized Orlicz-Morrey spaces $M^{Φ,φ}(\mathbb{R}^n)$. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on weights $φ(x,r)$ without assuming any monotonicity property of $φ(x,r)$ on $r$.