- Turkish Journal of Mathematics and Computer Science
- Vol: 14 Issue: 2
- An Extension of the Adams-type Theorem to the Vanishing Generalized Weighted Morrey Spaces
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 : 7 | Download : 3
Publication Date : 2022-12-30
Article Type : Research
Abstract :In this paper, we generalize Adams-type theorems given in [1,13] (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 $\\mathcal{\\mathcal{VM}}_{p,\\varphi^{\\frac{1}{p}}}(\\mathbb{R}^n, w)$ to another one $\\mathcal{\\mathcal{VM}}_{q,\\varphi^{\\frac{1}{q}}}(\\mathbb{R}^n, w)$ with $w \\in A_{p,q}$ for $1$ $p$; and from the vanishing generalized weighted Morrey spaces $\\mathcal{\\mathcal{VM}}_{1,\\varphi}(\\mathbb{R}^n, w)$ to the vanishing generalized weighted weak Morrey spaces $\\mathcal{\\mathcal{VWM}}_{q,\\varphi^{\\frac{1}{q}}}(\\mathbb{R}^n, w)$ 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