Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator

We consider the generalized shift operator, associated with the Dunkl operator Λα(f)(x)=(d/dx)f(x)+((2α+1)/x)((f(x)-f(-x))/2), α>-1/2. We study some embeddings into the Morrey space (D-Morrey space) Lp,λ,α, 0≤λ<2α+2 and modified Morrey space (modified D-Morrey space) L̃p,λ,α associated with the Dunkl operator on ℝ. As applications we get boundedness of the fractional maximal operator Mβ, 0≤β<2α+2, associated with the Dunkl operator (fractional D-maximal operator) from the spaces Lp,λ,α to L∞(ℝ) for p=(2α+2-λ)/β and from the spaces L̃p,λ,α(ℝ) to L∞(ℝ) for (2α+2-λ)/β≤p≤(2α+2)/β

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)

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

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

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

FRACTIONAL MAXIMAL OPERATOR AND ITS COMMUTATORS IN GENERALIZED MORREY SPACES ON HEISENBERG GROUP

In this paper we study the boundedness of the fractional maximal operator M-alpha on Heisenberg group H-n in the generalized Morrey spaces M-p,(phi)(H-n). We shall give a characterization for the strong and weak type Spanne and Adams type boundedness of M-alpha on the generalized Morrey spaces, respectively. Also we give a characterization for the Spanne and Adams type boundedness of fractional maximal commutator operator M(b,alpha )on the generalized Morrey spaces.1st Azerbaijan-Russia Joint Grant Competition [EIF-BGM-4-RFTF-1/2017-21/01/1]The authors thank the anonymous referees for careful reading of the paper and very useful comments. The research of V.S. Guliyev was partially supported by the grant of the 1st Azerbaijan-Russia Joint Grant Competition (Agreement number no. EIF-BGM-4-RFTF-1/2017-21/01/1)

Characterizations for the Nonsingular Integral Operator and its Commutators on Generalized Orlicz-Morrey Spaces

We show continuity in generalized Orlicz-Morrey spaces M (Phi,phi) (R-+(n)) of nonsingular integral operators and its commutators with BMO functions. We shall give necessary and sufficient conditions for the boundedness of the nonsingular integral operator and its commutators on generalized Orlicz-Morrey spaces M Phi,phi (R-+(n)).Ahi Evran University Scientific Research Project [FEF.A3.16.024]; Presidium of National Academy of Sciences of AzerbaijanWe thank the referee(s) for carefully reading our paper and useful comments. The research of V.S. Guliyev was partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.024) and by the grant of Presidium of National Academy of Sciences of Azerbaijan 2015

Fractional maximal operator and its commutators in generalized morrey spaces on Heisenberg group

In this paper we study the boundedness of the fractional maximal operator M ? on Heisenberg group H n in the generalized Morrey spaces M p,? (H n ). We shall give a characterization for the strong and weak type Spanne and Adams type boundedness of M ? on the generalized Morrey spaces, respectively. Also we give a characterization for the Spanne and Adams type boundedness of fractional maximal commutator operator M b,? on the generalized Morrey spaces. © 2018, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved

Characterization of Parabolic Fractional Integral and Its Commutators in Parabolic Generalized Orlicz-Morrey Spaces

In this paper, we give necessary and sufficient condition for the Adams type boundedness of parabolic fractional integral and its commutators in parabolic generalized Orlicz-Morrey spaces.grant of the 1st Azerbaijan - Russia Joint Grant Competition [EIF-BGM-4-RFTF-1/2017-21/01/1]We thank the referee(s) for carefully reading our paper and useful comments. The research of V. S. Guliyev was partially supported by the grant of the 1st Azerbaijan - Russia Joint Grant Competition (Agreement number no. EIF-BGM-4-RFTF-1/2017-21/01/1)

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