The Two-Type Estimates for The Boundedness of Generalized Fractional Maximal Operator on The Generalized Weighted Local  Morrey Spaces

Abdulhamit KÜÇÜKASLAN

Makale detayları

The Two-Type Estimates for The Boundedness of Generalized Fractional Maximal Operator on The Generalized Weighted Local Morrey Spaces

Yazarlar:

Abdulhamit KÜÇÜKASLAN

Yayıncı:

Matematikçiler Derneği

Ana Başlıklar:

Matematik

Dergi:

Turkish Journal of Mathematics and Computer Science 2020 Vol.12 Issue 1, pp.56-65

Belge Tipi:

Makale

Yayın Tarihi:

6/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000638485

Sıklık:

İki Yıllık

eISSN:

2148-1830

Özet:

 


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 MρMρM_{\rho} on the generalized weighted local Morrey spaces M{x0}p,φ(wp)Mp,φ{x0}(wp)M^{\{x_0\}}_{p,\varphi}(w^{p}) and generalized weighted Morrey spaces Mp,φ1p(w)Mp,φ1p(w)M_{p,\varphi^{\frac{1}{p}}}(w), including weak estimates. We prove the Spanne type boundedness of the generalized fractional maximal operator MρMρM_{\rho} from generalized  weighted local Morrey spaces M{x0}p,φ1(wp)Mp,φ1{x0}(wp)M^{\{x_0\}}_{p,\varphi_{1}}(w^{p}) to the weighted weak space WM{x0}q,φ2(wq)WMq,φ2{x0}(wq)WM^{\{x_0\}}_{q,\varphi_2}(w^{q})  for 1≤p<q<∞1≤p<q<∞1\leq p< q<\infty and from M{x0}p,φ1(wp)Mp,φ1{x0}(wp)M^{\{x_0\}}_{p,\varphi_1}(w^{p}) to another space M{x0}q,φ2(wq)Mq,φ2{x0}(wq)M^{\{x_0\}}_{q,\varphi_{2}}(w^{q}) for 1<p<q<∞1<p<q<∞1< p< q<\infty with wq∈A1+qp′wq∈A1+qp′w^{q} \in A_{1+\frac{q}{p'}}. We also prove the Adams type boundedness of MρMρM_{\rho} from Mp,φ1p(w)Mp,φ1p(w)M_{p,\varphi^{\frac{1}{p}}}(w) to the weighted weak space WMq,φ1q(w)WMq,φ1q(w)WM_{q,\varphi^{\frac{1}{q}}}(w)  for $1\leq pIn all cases the conditions for the boundedness of the operator MρMρM_{\rho} are given in terms of supremal-type integral inequalities on the all φφ\varphi functions and rrr which do not assume any assumption on monotonicity of 	φ1(x,r)φ1(x,r)\varphi_1(x,r), φ2(x,r)φ2(x,r)\varphi_2(x,r) and 	φ(x,r)φ(x,r)\varphi(x,r) in rrr.

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Makale detayları

The Two-Type Estimates for The Boundedness of Generalized Fractional Maximal Operator on The Generalized Weighted Local Morrey Spaces

Yazarlar: Abdulhamit KÜÇÜKASLAN

Yayıncı: Matematikçiler Derneği

Ana Başlıklar: Matematik

Dergi: Turkish Journal of Mathematics and Computer Science 2020 Vol.12 Issue 1, pp.56-65

Belge Tipi: Makale

Yayın Tarihi: 6/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000638485

Sıklık: İki Yıllık

eISSN: 2148-1830

Sayı

Yazarlar:

Abdulhamit KÜÇÜKASLAN

Yayıncı:

Matematikçiler Derneği

Ana Başlıklar:

Matematik

Dergi:

Turkish Journal of Mathematics and Computer Science 2020 Vol.12 Issue 1, pp.56-65

Belge Tipi:

Makale

Yayın Tarihi:

6/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000638485

Sıklık:

İki Yıllık

eISSN:

2148-1830