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 $1$<$p$<$\infty,\ q$>$p$; 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 $A_{p,q}$.
Generalized fractional maximal operator Vanishing generalized weighted Morrey space Muckenhoupt-Weeden classes Muckenhoupt-Weeden class
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Erken Görünüm Tarihi | 23 Aralık 2022 |
Yayımlanma Tarihi | 30 Aralık 2022 |
Yayımlandığı Sayı | Yıl 2022 Cilt: 14 Sayı: 2 |