An Extension of the Adams-type Theorem to the Vanishing Generalized Weighted Morrey Spaces

Authors : Abdulhamit KÜÇÜKASLAN

Pages : 384-390

Doi:10.47000/tjmcs.1004212

View : 51 | Download : 9

Publication Date : 2022-12-30

Article Type : Research Paper

Abstract :In this paper, we generalize Adams-type theorems given in [1,13] insert ignore into journalissuearticles values(which are the following Theorem A and Theorem B, respectively); to the vanishing generalized weighted Morrey spaces. We prove the Adams-type boundedness of the generalized fractional maximal operator $M_{\\rho}$ from the vanishing generalized weighted Morrey spaces $\\mathcal{\\mathcal{VM}}_{p,\\varphi^{\\frac{1}{p}}}insert ignore into journalissuearticles values(\\mathbb{R}^n, w);$ to another one $\\mathcal{\\mathcal{VM}}_{q,\\varphi^{\\frac{1}{q}}}insert ignore into journalissuearticles values(\\mathbb{R}^n, w);$ with $w \\in A_{p,q}$ for $1$ $p$; and from the vanishing generalized weighted Morrey spaces $\\mathcal{\\mathcal{VM}}_{1,\\varphi}insert ignore into journalissuearticles values(\\mathbb{R}^n, w);$ to the vanishing generalized weighted weak Morrey spaces $\\mathcal{\\mathcal{VWM}}_{q,\\varphi^{\\frac{1}{q}}}insert ignore into journalissuearticles values(\\mathbb{R}^n, w);$ with $w \\in A_{1,q}$ for $p=1,\\ 1$<$ q$<$\\infty$. The all weight functions belong to Muckenhoupt-Weeden classes $A_{p,q}$.
Keywords : Generalized fractional maximal operator, Vanishing generalized weighted Morrey space, Muckenhoupt Weeden classes, Muckenhoupt Weeden class

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