arXiv subjects

Abdulhamit Kucukaslan

Publications and source records attributed to Abdulhamit Kucukaslan.

3 recordsLinked to original sources

arXiv2021

Maximal and fractional maximal operators in the Lorentz Morrey spaces and their applications to the Bochner Riesz and Schrodinger type operators

The aim of this paper is to obtain boundedness conditions for the maximal function Mf and to prove the necessary and sufficient conditions for the fractional maximal oparator Ma in the Lorentz Morrey spaces which are a new class of functions. We get our main results by using the obtained sharp rearrangement estimates. The obtained results are applied to the boundedness of particular operators such as the Bochner Riesz operator and the Schrodinger type operators in the Lorentz Morrey spaces, where the nonnegative potential V belongs to the reverse Holder class.

math.FA↗

arXiv2021

Two type Estimates for the Boundedness of Generalized Riesz Potential Operator in the Generalized Weighted Local Morrey Spaces

In this paper, we prove the Spanne-type boundedness of the generalized Riesz potential operator from the one generalized weighted local Morrey spaces to the another one, and from the generalized weighted local Morrey spaces to the weak generalized weighted local Morrey spaces. We also prove the Adams-type boundedness of the operator from the weighted spaces to the another one, and from the weighted spaces to the weak weighted spaces.

math.FA↗

arXiv2018

An extension of Muchenhoupt-Wheeden theorem to generalized weighted (central) Morrey spaces

In this paper we find the condition on function $ω$ and weight $v$ which ensures the equivalency of norms of the Riesz potential and the fractional maximal function in generalized weighted Morrey spaces ${\mathcal M}_{p,ω}({\mathbb R}^n,v)$ and generalized weighted central Morrey spaces $\dot{\mathcal M}_{p,ω}({\mathbb R}^n,v)$, when $v$ belongs to Muckenhoupt $A_{\infty}$-class.

math.FA↗