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Ferit Gurbuz

Publications and source records attributed to Ferit Gurbuz.

At least 19 recordsLinked to original sources
arXiv2026

Endpoint and Interpolation Estimates for Higher-Order Commutators of Rough Fractional Maximal Operators with Variable Kernels on Variable Exponent Morrey Spaces

This paper investigates the higher-order commutators generated by fractional maximal operators with rough, spatially dependent kernels in the framework of variable exponent Morrey spaces. Under minimal log-H\"older continuity assumptions on the variable exponent profiles and suitable geometric constraints on the Morrey-type weights, we establish comprehensive strong interior boundedness results between the appropriate spaces. We further analyze the critical endpoint boundary configurations where classical strong-type boundedness fails due to Luxemburg norm blow-up, proving that a corresponding sharp weak-type estimate remains structurally valid and revealing the underlying transitions between different boundedness regimes. In addition, an abstract real interpolation framework of Grafakos--Martell type is developed to bridge these endpoint and interior strong estimates, thereby recovering a full continuous scale of intermediate regularity properties. These results extend the classical harmonic analysis scheme to a broader nonhomogeneous setting and provide new insights into the continuous interplay between rough kernels, variable exponents, and local weighted growth conditions.

math.FA↗
arXiv2026

Weak and Strong Convergence of Implicit Iterations for Lipschitzian Hemi-Contractive and {\alpha}-Hemi-Contractive Semigroups in Banach Spaces

We investigate an implicit iterative scheme for approximating common fixed points of one-parameter semigroups generated by Lipschitzian hemi-contractive and {\alpha}-hemi-contractive mappings on closed convex subsets of Banach spaces. Under suitable conditions on the control sequences, we establish weak convergence of the proposed iteration in uniformly convex Banach spaces satisfying Opial's condition. Furthermore, strong convergence results are obtained in general Banach spaces without imposing uniform convexity assumptions. The analysis is based on a careful use of recursive inequality techniques and weak convergence principles, allowing us to extend several known results in the literature. In particular, the proposed framework provides a unified approach that encompasses important classes of nonlinear operators, including pseudocontractive and demicontractive mappings, as special cases of hemi-contractive semigroups. Finally, we apply our results to nonlinear evolution, variational inequality, and nonlinear integral equations to demonstrate their broad applicability.

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arXiv2025

The boundedness of rough generalized commutators with Lipschitz functions on homogeneous variable exponent Herz type spaces

With the development of science, many nonlinear problems have emerged. At this time, the classical function space has certain restrictions. For example, it has lost its effectiveness for nonlinear problems under nonstandard growth conditions. In the process of studying such nonlinear problems, scholars are paying more and more attention to the transition from classical function space to variable exponent function space. Also, there is a big difference between variable exponent space and classical function space, mainly because variable exponent function space has lost translation invariance. This difference leads to many properties that hold in classical space no longer hold in variable exponent space. It is important to emphasize that variable exponent function spaces are a fundamental building block in harmonic analysis. In recent years, there has been a growing interest in the study of function spaces equipped with variable exponents, leading to the development of a new framework known as variable exponent analysis. These spaces provide a powerful tool for analyzing functions with variable growth or decay rates and have found applications in various areas of mathematics, including partial differential equations, harmonic analysis and image processing. One can better understand the heterogeneity and complexity inherent in many real world phenomena by taking into consideration the theory of variable exponent function spaces. Thus, by using certain properties of Lipschitz functions and variable exponents, in this article, we establish the boundedness of a class of rough generalized commutators with Lipschitz functions on homogeneous variable exponent Herz and Herz-Morrey spaces.

math.AP↗
arXiv2025

Some norm inequalities for commutators generated by the Riesz potentials on homogeneous variable exponent Herz-Morrey-Hardy spaces

In harmonic analysis, the studies of inequalities of classical operators (= singular, maximal, Riesz potentials etc.) in various function spaces have a very important place. The maturation of many topics in the field of harmonic analysis, as a result of various needs and developments to respond to the problems of the time, has also led to the emergence of many studies and works on these topics. In [3], under some conditions, the boundedness of Riesz potential on homogeneous variable exponent Herz-Morrey-Hardy spaces has been given. Inspired by the work of [3], in this work, by the atomic decompositions, we obtain the boundedness of commutators generated by the Riesz potentials on homogeneous variable exponent Herz-Morrey-Hardy spaces.

math.AP↗
arXiv2024

Some Inequalities for Riesz Potential on Homogeneous Variable Exponent Herz-Morrey-Hardy Spaces

In harmonic analysis, studies of inequalities of Riesz potential in various function spaces have a very important place. Variable exponent Morrey type spaces and the examines of the boundedness of such operators on these spaces have an important place in harmonic analysis and have become an interesting field. In this work, we obtain the boundedness of Riesz potential on homogeneous variable exponent Herz-Morrey-Hardy spaces under some conditions.

math.FA↗
arXiv2019

Weak And Strong Boundedness For P-adic Fractional Hausdorff Operator And Its Commutator

In this paper, boundedness of Hausdorff operator on weak central Morrey space is obtained. Furthermore, we investigate the weak bounds of p- adic fractional Hausdorff Operator on weighted p-adic weak Lebesgue Space. We also obtain the sufficient condition of commutators of p-adic fractional Hausdorff Operator by taking symbol function from Lipschitz space. Moreover, strong type estimates for fractional Hausdorff Operator and its commutator on weighted p-adic Lorentz space are also acquired.

math.FA↗
arXiv2018

On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product L^{p} and weighted L^{p} spaces

The aim of this paper is to get the product Lp-estimates, weighted estimates and two-weighted estimates for rough multilinear fractional integral operators and rough multi-sublinear fractional maximal operators, respectively. The author also studies two-weighted weak type estimate on product Lp (Rn) for rough multi-sublinear fractional maximal operators. In fact, this article is the rough kernel versions of [4, 5]' s results.

math.CA↗
arXiv2017

A note for some parabolic multilinear commutators generated by a class of parabolic maximal and linear operators with rough kernel on the parabolic generalized local Morrey spaces

In this paper, we give the boundedness of some parabolic multilinear commutators generated by a class of parabolic maximal and linear operators with rough kernel and parabolic local Campanato functions on the parabolic generalized local Morrey spaces, respectively. Indeed, the results in this paper are extensions of some known results.

math.FA↗
arXiv2016

Fractional type multilinear commutators generated by fractional integral with rough variable kernel and local Campanato functions on generalized vanishing local Morrey spaces

In this paper, we consider the boundedness of fractional type multilinear commutators generated by fractional integral with rough variable kernel and local Campanato functions on both generalized local (central) Morrey spaces and generalized vanishing local Morrey spaces, under generic size conditions which are satisfied by most of the operators in harmonic analysis, respectively.

math.FA↗