Some notes on commutators of the fractional maximal and Riesz potential operators on Orlicz spaces

The main focus of this paper is commutators and maximal commutators on Orlicz spaces for fractional maximal functions and Riesz potential. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness in less restrictive terms

Fractional maximal function and its commutators on Orlicz spaces

In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $M_{\alpha}$ on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator $M_{b,\alpha}$ and nonlinear commutator of fractional maximal operator $[b,M_{\alpha}]$ on Orlicz spaces, when $b$ belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.Comment: 15 pages, Anal. Math. Phys.(to appear

Commutators of fractional maximal operator on generalized Orlicz-Morrey spaces

WOS: 000425301900011In the present paper, we shall give necessary and sufficient conditions for the Spanne and Adams type boundedness of the commutators of fractional maximal operator on generalized Orlicz-Morrey spaces, respectively. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators.Ahi Evran UniversityAhi Evran University [FEF.A3.16.024]; Ministry of Education and Science of the Russian FederationMinistry of Education and Science, Russian Federation [02.a03.21.0008]The research of V.S. Guliyev and F. Deringoz is partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.024). The research of V.S. Guliyev is partially supported by the Ministry of Education and Science of the Russian Federation (the Agreement No. 02.a03.21.0008)

A characterization for Adams-type boundedness of the fractional maximal operator on generalized Orlicz-Morrey spaces

WOS: 000399466500003In the present paper, we shall give a characterization for weak/strong Adams-type boundedness of the fractional maximal operator on generalized Orlicz-Morrey spaces.Ahi Evran University Scientific Research ProjectAhi Evran University [FEF.A3.16.024]; grant of Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS)The research of V.S. Guliyev and F. Deringoz is partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.024). The research of V.S. Guliyev is partially supported by the grant of Presidium Azerbaijan National Academy of Science 2015. We thank the referee(s) for careful reading the paper and useful comments

Non-smooth Atomic Decompositions for Generalized Orlicz-Morrey Spaces of the Third Kind

WOS: 000382700200006We deal with the generalized Orlicz-Morrey space of the third kind and consider the decomposition method. Also we characterize its predual space. Some maximal estimates for generalized Orlicz-Morrey spaces of the third kind are also obtained by using the weighted Hardy operators. As an application, we consider the Olsen inequality, which is a bilinear estimate on the fractional integral operator. As an appendix, we consider a general form of the vector-valued boundedness of the Hardy-Littlewood maximal operator, where in the definition of depends on as well. This paper contains a remedy for the mistake in the proof of the Olsen inequality of the 2014 paper by the second author (Iida et al. in Z. Anal. Anwend. 33(2):149-170, 2014).Science Development Foundation under the President of the Republic of AzerbaijanScience Development Foundation (SDF) - Azerbaijan [EIF-2013-9(15)-46/10/1]; Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS)The research of V. Guliyev was partially supported by the grant of Science Development Foundation under the President of the Republic of Azerbaijan, Grant EIF-2013-9(15)-46/10/1 and by the grant of Presidium Azerbaijan National Academy of Science 2015. This paper is written during the stay of Y. Sawano in Ahi Evran University. Y. Sawano is thankful to Ahi Evran University for this support of the stay there. Y. Sawano is thankful to Professor Jie Xiao for his pointing out that (7.18) is correct under some restricted conditions. The authors are thankful to Professor Mitsuo Izuki at Okayama University for his careful reading of the manuscript

Negative magneto-resistance of electron gas in a quantum well with parabolic potential

We have studied the electrical conductivity of the electron gas in parallel electric and magnetic fields directed along the plane of a parabolic quantum well (across the profile of the potential). We found a general expression for the electrical conductivity applicable for any magnitudes of the magnetic field and the degree of degeneration of the electron gas. A new mechanism of generation of the negative magnetoresistance has been revealed. It has been shown that in a parabolic quantum well with a non-degenerated electron gas the negative magnetoresistance results from spin splitting of the levels of the size quantization.Comment: 15 pages, 3 figure

Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces

We consider local "complementary" generalized Morrey spaces M-c({x0})p(.).omega (Omega) in which the p-means of function are controlled over Omega \ B(x(0), r) instead of B(x(0), r), where Omega subset of R-n is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function omega(r) defining the "complementary" Morrey-type norm. In the case where omega is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type M-c({x0})p(.).omega (Omega) -> M-c({x0})p(.).omega (Omega)-theorem for the potential operators I-alpha(.), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities-on omega(r), which do not assume any assumption on monotonicity of omega(r).Science Development Foundation under the President of the Republic of Azerbaijan [EIF-2010-1(1)-40/06-1]; Scientific and Technological Research Council of Turkey (TUBITAK) [110T695]info:eu-repo/semantics/publishedVersio

dReDBox: Materializing a full-stack rack-scale system prototype of a next-generation disaggregated datacenter

Current datacenters are based on server machines, whose mainboard and hardware components form the baseline, monolithic building block that the rest of the system software, middleware and application stack are built upon. This leads to the following limitations: (a) resource proportionality of a multi-tray system is bounded by the basic building block (mainboard), (b) resource allocation to processes or virtual machines (VMs) is bounded by the available resources within the boundary of the mainboard, leading to spare resource fragmentation and inefficiencies, and (c) upgrades must be applied to each and every server even when only a specific component needs to be upgraded. The dRedBox project (Disaggregated Recursive Datacentre-in-a-Box) addresses the above limitations, and proposes the next generation, low-power, across form-factor datacenters, departing from the paradigm of the mainboard-as-a-unit and enabling the creation of function-block-as-a-unit. Hardware-level disaggregation and software-defined wiring of resources is supported by a full-fledged Type-1 hypervisor that can execute commodity virtual machines, which communicate over a low-latency and high-throughput software-defined optical network. To evaluate its novel approach, dRedBox will demonstrate application execution in the domains of network functions virtualization, infrastructure analytics, and real-time video surveillance.This work has been supported in part by EU H2020 ICTproject dRedBox, contract #687632.Peer ReviewedPostprint (author's final draft

On the effect of N-GaN/P-GaN/N-GaN/P-GaN/N-GaN built-in junctions in the n-GaN layer for InGaN/GaN light-emitting diodes

Cataloged from PDF version of article.N-GaN/P-GaN/N-GaN/P-GaN/N-GaN (NPNPN-GaN) junctions embedded between the n-GaN region and multiple quantum wells (MQWs) are systematically studied both experimentally and theoretically to increase the performance of InGaN/GaN light emitting diodes (LEDs) in this work. In the proposed architecture, each thin P-GaN layer sandwiched in the NPNPN-GaN structure is completely depleted due to the built-in electric field in the NPNPN-GaN junctions, and the ionized acceptors in these P-GaN layers serve as the energy barriers for electrons from the n-GaN region, resulting in a reduced electron over flow and enhanced the current spreading horizontally in the n-GaN region. These lead to increased optical output power and external quantum efficiency (EQE) from the proposed device. (C) 2014 Optical Society of Americ