scholarly journals Necessary and sufficient conditions for the boundedness of B-Riesz potential in the B-Morrey spaces

2008 ◽  
Vol 347 (1) ◽  
pp. 113-122 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Javanshir J. Hasanov
Keyword(s):  
Riesz Potential ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

scholarly journals Weighted Hardy and Potential Operators in Morrey Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Natasha Samko
Keyword(s):  
Riesz Potential ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Potential Operator ◽  
Potential Operators ◽  
Riesz Potential Operator ◽  
Power Weights ◽  
The One ◽  
Necessary And Sufficient ◽  
Hardy Type Operators

We study the weightedp→q-boundedness of Hardy-type operators in Morrey spacesℒp,λ(ℝn) (orℒp,λ(ℝ+1) in the one-dimensional case) for a class of almost monotonic weights. The obtained results are applied to a similar weightedp→q-boundedness of the Riesz potential operator. The conditions on weights, both for the Hardy and potential operators, are necessary and sufficient in the case of power weights. In the case of more general weights, we provide separately necessary and sufficient conditions in terms of Matuszewska-Orlicz indices of weights.

scholarly journals Characterizations for the potential operators on Carleson curves in local generalized Morrey spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 1317-1331
Author(s):  
Vagif Guliyev ◽  
Hatice Armutcu ◽  
Tahir Azeroglu
Keyword(s):  
Morrey Space ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Necessary And Sufficient Conditions ◽  
Potential Operator ◽  
Generalized Morrey Space ◽  
Generalized Morrey Spaces ◽  
Potential Operators ◽  
Boundedness Criterion ◽  
Necessary And Sufficient

Abstract In this paper, we give a boundedness criterion for the potential operator { {\mathcal I} }^{\alpha } in the local generalized Morrey space L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the generalized Morrey space {M}_{p,\varphi }(\text{Γ}) defined on Carleson curves \text{Γ} , respectively. For the operator { {\mathcal I} }^{\alpha } , we establish necessary and sufficient conditions for the strong and weak Spanne-type boundedness on L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the strong and weak Adams-type boundedness on {M}_{p,\varphi }(\text{Γ}) .

Riesz potential in the local Morrey–Lorentz spaces and some applications

2020 ◽  
Vol 27 (4) ◽  
pp. 557-567
Author(s):  
Vagif S. Guliyev ◽  
Abdulhamit Kucukaslan ◽  
Canay Aykol ◽  
Ayhan Serbetci
Keyword(s):  
Maximal Operator ◽  
Riesz Potential ◽  
Sufficient Conditions ◽  
Lorentz Spaces ◽  
Necessary And Sufficient Conditions ◽  
Analytic Semigroups ◽  
Fractional Powers ◽  
Marcinkiewicz Operator ◽  
Fractional Maximal Operator ◽  
Necessary And Sufficient

AbstractIn this paper, the necessary and sufficient conditions are found for the boundedness of the Riesz potential {I_{\alpha}} in the local Morrey–Lorentz spaces {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})}. This result is applied to the boundedness of particular operators such as the fractional maximal operator, fractional Marcinkiewicz operator and fractional powers of some analytic semigroups on the local Morrey–Lorentz spaces {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})}.

scholarly journals Necessary and Sufficient Conditions for the Boundedness of Dunkl-Type Fractional Maximal Operator in the Dunkl-Type Morrey Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-10
Author(s):  
Emin Guliyev ◽  
Ahmet Eroglu ◽  
Yagub Mammadov
Keyword(s):  
Maximal Operator ◽  
Morrey Space ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Necessary And Sufficient Conditions ◽  
Dunkl Operator ◽  
Generalized Shift Operator ◽  
Fractional Maximal Operator ◽  
Generalized Shift ◽  
Necessary And Sufficient

We consider the generalized shift operator, associated with the Dunkl operator , . We study the boundedness of the Dunkl-type fractional maximal operator in the Dunkl-type Morrey space , . We obtain necessary and sufficient conditions on the parameters for the boundedness , from the spaces to the spaces , , and from the spaces to the weak spaces , . As an application of this result, we get the boundedness of from the Dunkl-type Besov-Morrey spaces to the spaces , , , , , and .

scholarly journals Necessary and sufficient conditions for the boundedness of the anisotropic Riesz potential in anisotropic modified Morrey spaces

2013 ◽  
Vol 21 (2) ◽  
pp. 111-130
Author(s):  
Malik S. Dzhabrailov ◽  
Sevinc Z. Khaligova
Keyword(s):  
Maximal Operator ◽  
Morrey Space ◽  
Riesz Potential ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Potential Operator ◽  
Fractional Maximal Operator ◽  
Riesz Potential Operator ◽  
Necessary And Sufficient ◽  
Limiting Case

Abstract We prove that the anisotropic fractional maximal operator Mα,σ and the anisotropic Riesz potential operator Iα,σ, 0 < α < ∣σ∣ are bounded from the anisotropic modified Morrey space L̃1,b,σ(Rn) to the weak anisotropic modified Morrey space WL̃q,b,σ(Rn) if and only if, α/|σ|≤1-1/q≤α/(|σ|(1-b)) and from L̃p,b,σ(Rn) to L̃q,b,σ(Rn) if and only if, α/|σ| ≤ 1/p-1/q≤α ((1-b) |σ|). In the limiting case we prove that the operator Mα,σ is bounded from L̃p,b,σ(Rn) to L∞ (Rn) and the modified anisotropic Riesz potential operator Ĩα,σ is bounded from L̃p,b,σ(Rn) to BMOσ(Rn).

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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