Characterizations for the fractional integral operators in generalized Morrey spaces on Carnot groups

WOS: 000418838500011In this paper, we study the boundedness of the fractional integral operator I (alpha) on Carnot group G in the generalized Morrey spaces M (p, phi) (G). We shall give a characterization for the strong and weak type boundedness of I (alpha) on the generalized Morrey spaces, respectively. As applications of the properties of the fundamental solution of sub-Laplacian L on G, we prove two Sobolev-Stein embedding theorems on generalized Morrey spaces in the Carnot group setting.grant of the Presidium of the Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS); Ahi Evran University Scientific Research ProjectAhi Evran University [FEF.A3.16.024]The research of V. S. Guliyev was supported in part by the 2015 grant of the Presidium of the Azerbaijan National Academy of Science and by the Ahi Evran University Scientific Research Project under grant FEF.A3.16.024)

Fractional weighted spherical mean and maximal inequality for the weighted spherical mean and its application to singular PDE

In this paper we establish a mean value property for the functions which is satisfied to Laplace-Bessel equation. Our results involve the generalized divergence theorem and the second Green’s identities relating the bulk with the boundary of a region on which differential Bessel operators ac

Maximal operator in variable exponent generalized morrey spaces on quasi-metric measure space

We consider generalized Morrey spaces on quasi-metric measure spaces , in general unbounded, with variable exponent p(x) and a general function defining the Morrey-type norm. No linear structure of the underlying space X is assumed. The admission of unbounded X generates problems known in variable exponent analysis. We prove the boundedness results for maximal operator known earlier only for the case of bounded sets X. The conditions for the boundedness are given in terms of the so called supremal inequalities imposed on the function , which are weaker than Zygmund-type integral inequalities often used for characterization of admissible functions . Our conditions do not suppose any assumption on monotonicity of in r

Analysis of microbial populations in plastic-soil systems after exposure to high poly(butylene succinate-co-adipate) load using high-resolution molecular technique

BACKGROUND: Bio-based and biodegradable plastics are considered as plastics of the future owing to their ability to decompose under various environmental conditions. However, their effects on the soil microbiome are poorly characterised. In this study, we aimed to investigate the effects of an important bio-based and biodegradable plastic, polybutylene succinate-co-adipate (PBSA), on soil microbial diversity and community composition using high-resolution molecular technique (Illumina sequencing) targeting all three microbial domains: archaea, bacteria, and fungi. RESULTS: Adding high load of PBSA to soil (6% (w/w)) caused a significant decline in archaeal (13%) and fungal (45%) richness and substantial changes in both bacterial (Proteobacteria, Actinobacteria, and Acidobacteria) and fungal (Eurotiomycetes, Sordariomycetes, Leotiomycetes, and Dothideomycetes) community composition compared with no PBSA addition to soil. The combined effects of PBSA and (NH₄)₂SO₄ fertilisation on the soil microbiome were much greater than the effects of PBSA alone. We only detected opportunistic human pathogens in low abundance on PBSA and in the surrounding soil. However, some plant pathogenic fungi were detected and/or enriched on the PBSA films and in surrounding soil. Apart from plant pathogens, many potential microbial control agents and plant growth-promoting microorganisms were also detected/enriched owing to PBSA addition. Adding high load of PBSA together with (NH₄)₂SO₄ fertilisation can either eliminate some plant pathogens or enrich specific pathogens, especially Fusarium solani, which is economically important. CONCLUSIONS: We conclude that high load of bio-based and biodegradable PBSA plastic may negatively affect soil microbiome

Variable exponent Besov-Morrey spaces

In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.publishe

Technical Design Report for the PANDA Solenoid and Dipole Spectrometer Magnets

This document is the Technical Design Report covering the two large spectrometer magnets of the PANDA detector set-up. It shows the conceptual design of the magnets and their anticipated performance. It precedes the tender and procurement of the magnets and, hence, is subject to possible modifications arising during this process.Comment: 10 pages, 14MB, accepted by FAIR STI in May 2009, editors: Inti Lehmann (chair), Andrea Bersani, Yuri Lobanov, Jost Luehning, Jerzy Smyrski, Technical Coordiantor: Lars Schmitt, Bernd Lewandowski (deputy), Spokespersons: Ulrich Wiedner, Paola Gianotti (deputy

Performance of the first prototype of the CALICE scintillator strip electromagnetic calorimeter

A first prototype of a scintillator strip-based electromagnetic calorimeter was built, consisting of 26 layers of tungsten absorber plates interleaved with planes of 45x10x3 mm3 plastic scintillator strips. Data were collected using a positron test beam at DESY with momenta between 1 and 6 GeV/c. The prototype's performance is presented in terms of the linearity and resolution of the energy measurement. These results represent an important milestone in the development of highly granular calorimeters using scintillator strip technology. This technology is being developed for a future linear collider experiment, aiming at the precise measurement of jet energies using particle flow techniques

The Time Structure of Hadronic Showers in highly granular Calorimeters with Tungsten and Steel Absorbers

The intrinsic time structure of hadronic showers influences the timing capability and the required integration time of hadronic calorimeters in particle physics experiments, and depends on the active medium and on the absorber of the calorimeter. With the CALICE T3B experiment, a setup of 15 small plastic scintillator tiles read out with Silicon Photomultipliers, the time structure of showers is measured on a statistical basis with high spatial and temporal resolution in sampling calorimeters with tungsten and steel absorbers. The results are compared to GEANT4 (version 9.4 patch 03) simulations with different hadronic physics models. These comparisons demonstrate the importance of using high precision treatment of low-energy neutrons for tungsten absorbers, while an overall good agreement between data and simulations for all considered models is observed for steel.Comment: 24 pages including author list, 9 figures, published in JINS