The boundedness of Bessel–Riesz operators defined on Lebesgue spaces and Morrey in measure metric is discussed this research study. maximal operator traditional dyadic decomposition are used to study the Bessel-Riesz operators. We investigate interaction between kernel space parameters get results see how affects kernel-bound

In this paper, we introduce the local and global mixed Morrey-type spaces show some properties. Besides, investigate boundedness of fractional integral operators $$I_\alpha $$ in these spaces. Firstly, sufficient necessary conditions mixed-norm Lebesgue for Then, prove $$I_{\alpha }$$ by Hardy operators’ weighted Furthermore, obtain corollaries.

As the development of singular integral operators, their commutators have been well studied(see [1][3-5][10-12]). Let T be the Calderón-Zygmund singular integral operator. A classical result of Coifman, Rocherberg and Weiss (see [3]) state that commutator [b, T ](f) = T (bf) − bT (f)(where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p < ∞. In [10-12], the sharp estimates for some multilinear comm...

and Applied Analysis 3 In literature, several authors have considered different kinds of weighted spaces of Morrey type and their applications to the study of elliptic equations, both in the degenerate case and in the nondegenerate one see e.g., 9–11 . In this paper, given a weight ρ in a class of measurable functions G Ω see § 6 for its definition , we prove that the corresponding weighted spa...

We consider generalized Morrey spaces Mp,ω R with a general function ω x, r defining the Morrey-type norm. We find the conditions on the pair ω1, ω2 which ensures the boundedness of the maximal operator and Calderón-Zygmund singular integral operators from one generalized Morrey space Mp,ω1 R to another Mp,ω2 R , 1 < p < ∞, and from the space M1,ω1 R to the weak space WM1,ω2 R . We also prove a...

The aim in this paper is to establish a new duality property of Morrey spaces and discover the complex interpolation space between Lebesgue spaces. For that purpose, N p , q s R n </msu...

In this paper, we prove the Spanne-Guliyev type boundedness of the generalized fractional integral operator Iρ from the vanishing generalized local Morrey spaces V LM {x0} p,φ1 to V LM {x0} q,φ2 , 1 < p < q < ∞, and from the space V LM {x0} 1,φ1 to the weak space VWLM {x0} q,φ2 , 1 < q < ∞. We also prove the Adams-Guliyev type boundedness of the operator Iρ from the vanishing generalized Morrey...

By applying the vector-valued inequalities for the Littlewood-Paley operators and their commutators on Lebesgue spaces with variable exponent, the boundedness of the Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g μ *-functions, and their commutators generated by BMO functions, is obtained on the Morrey spaces with variable exponent.

Morrey Spaces were first introduced by C.B. in 1938. space can be considered as a generalization of the Lebesgue spaces. spaces then generalized become spaces, weighted and One studies on is boundedness certain operators fractional integral. The integrals classical had been known. extensions operator was bounded purpose this study to investigate weight used Muckenhoupt class. results obtained s...