Two-type estimates for the boundedness of generalized Riesz potential operator in the generalized weighted local Morrey spaces

Küçükaslan, Abdulhamit

doi:10.32513/asetmj/1932200817

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2022

2023

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Cited by 4 publications

(2 citation statements)

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“…Lemma 3.1. ( [16]). Let w ∈ A p,q , 1 ≤ p < ∞, q > p, the function ρ satisfies the conditions(3.1)-(3.2), and f ∈ L loc 1 (R n , w).…”

Section: Preliminariesmentioning

confidence: 99%

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

Küçükaslan

2022

Turkish Journal of Mathematics and Computer Science

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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 $1$

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“…Lemma 3.1. ( [16]). Let w ∈ A p,q , 1 ≤ p < ∞, q > p, the function ρ satisfies the conditions(3.1)-(3.2), and f ∈ L loc 1 (R n , w).…”

Section: Preliminariesmentioning

confidence: 99%

“…Nakai [24] introduced the the generalized Morrey spaces M p,φ and proved the boundedness of the generalized fractional integral operator I ρ in these spaces. Nowadays many authors have been culminating important observations about these twooperators M ρ and I ρ especially in connection with Morrey-type spaces (see [3,10,[14][15][16]).…”

Section: Introductionmentioning

confidence: 99%