We prove the Spanne type boundedness of the generalized fractional maximal operator $M_{rho}$ from generalized weighted local Morrey spaces $M^{{x_0}}_{p,varphi_{1}}(w^{p})$ to the weighted weak space $WM^{{x_0}}_{q,varphi_2}(w^{q})$ for $1leq p< q
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we study two-type estimates which are the Spanne and Adams type estimates for the continuity properties of the generalized fractional maximal operator $M_{rho}$ on the generalized weighted local Morrey spaces $M^{{x_0}}_{p,varphi}(w^{p})$ and generalized weighted Morrey spaces $M_{p,varphi^{frac{1}{p}}}(w)$, including weak estimates.
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Key Findings & Data:In this paper, we study two-type estimates which are the Spanne and Adams type estimates for the continuity properties of the generalized fractional maximal operator $M_{rho}$ on the generalized weighted local Morrey spaces $M^{{x_0}}_{p,varphi}(w^{p})$ and generalized weighted Morrey spaces $M_{p,varphi^{frac{1}{p}}}(w)$, including weak estimates.
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Conclusion & Impact:We prove the Spanne type boundedness of the generalized fractional maximal operator $M_{rho}$ from generalized weighted local Morrey spaces $M^{{x_0}}_{p,varphi_{1}}(w^{p})$ to the weighted weak space $WM^{{x_0}}_{q,varphi_2}(w^{q})$ for $1leq p< q
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we study two-type estimates which are the Spanne and Adams type estimates for the continuity properties of the generalized fractional maximal operator $M_{rho}$ on the generalized weighted local Morrey spaces $M^{{x_0}}_{p,varphi}(w^{p})$ and generalized weighted Morrey spaces $M_{p,varphi^{frac{1}{p}}}(w)$, including weak estimates. We prove the Spanne type boundedness of the generalized fractional maximal operator $M_{rho}$ from generalized weighted local Morrey spaces $M^{{x_0}}_{p,varphi_{1}}(w^{p})$ to the weighted weak space $WM^{{x_0}}_{q,varphi_2}(w^{q})$ for $1leq p< q
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Cite This Article
KÜÇÜKASLAN, A. (2022). The Two-Type Estimates for The Boundedness of Generalized Fractional Maximal Operator on the Generalized Weighted Local Morrey Spaces. Turkish Journal of Mathematics and Computer Science, Cilt: 12 - Sayı: 1, 56–65. https://ajindex.com/articles/609115
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