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Öğe Characterization of Parabolic Fractional Integral and Its Commutators in Parabolic Generalized Orlicz-Morrey Spaces(Inst Math & Mechanics Azerbaijan, 2019) Eroglu, A.; Abasova, G. A.; Guliyev, V. S.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.Öğe Characterizations for the nonsingular integral operator and its commutators on generalized Orlicz-Morrey spaces(Azerbaijan Mathematical Society, 2017) Eroglu, A.; Guliyev, V.S.; Omarova, Mehriban N.We show continuity in generalized Orlicz-Morrey spaces M??(?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??(?n +). © 2010 AZJM All rights reserved.Öğe Characterizations for the Nonsingular Integral Operator and its Commutators on Generalized Orlicz-Morrey Spaces(Inst Math & Mechanics Azerbaijan, 2017) Eroglu, A.; Guliyev, V. S.; Omarova, M. N.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)).Öğe FRACTIONAL OSCILLATORY INTEGRAL OPERATORS AND THEIR COMMUTATORS ON GENERALIZED ORLICZ-MORREY SPACES OF THE THIRD KIND(L N GUMILYOV EURASIAN NATL UNIV, 2017) Eroglu, A.We deal with the generalized Orlicz-Morrey space M-Phi,M-phi of the third kind and consider the boundedness of the oscillatory integral operators and fractional oscillatory integral operators on M-Phi,M-phi. Some integral estimates for generalized Orlicz-Morrey spaces of the third kind are also obtained by using weighted Hardy operators. The corresponding commutators generated by BMO-functions are also considered.Öğe PARABOLIC FRACTIONAL MAXIMAL COMMUTATORS WITH BMO FUNCTION ON ORLICZ SPACES(Inst Applied Mathematics, 2024) Guliyev, V. S.; Eroglu, A.; Eroglu, G. A.In the note, we give necessary and sufficient conditions for the boundedness of the parabolic fractional maximal commutators M-b,alpha(P) on Orlicz spaces L-Phi (R-n) when b belongs to BMO (R-n) spaces, by which some new characterizations for BMO(R-n) spaces is obtained.Öğe Spanne Type Characterization of Parabolic Fractional Maximal Function and Its Commutators in Parabolic Generalized Orlicz–Morrey Spaces(Springer, 2021) Guliyev, V.S.; Eroglu, A.; Abasova, G.A.In this paper, we shall give necessary and sufficient conditions for the Spanne type boundedness of the parabolic fractional maximal operator and its commutators on parabolic generalized Orlicz–Morrey spaces, res-pectively. 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. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.Öğe Two weighted inequalities for fractional integrals on Laguerre hypergroup(Taylor & Francis Ltd, 2017) Eroglu, A.; Hajibayov, M. G.Let K = [0,infinity) x R be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group, vertical bar.vertical bar its homogeneous norm and Q its homogeneous dimension. In this paper we prove the two weighted inequality for fractional integrals I-beta on K. The obtained result is an analog of the Heinig result [Heinig HP. Weighted norm inequalities for classes of operators. Indiana Univ Math J. 1984;33(4):573-582] for fractional integrals on Laguerre hypergroup. Furthermore, the Stein-Weiss inequality for I-beta is proved as an application of this result.
