Papers by Vagif S. Guliyev
Deleted Journal, 2024
We give necessary and sufficient conditions for the boundedness of the anisotropic fractional max... more We give necessary and sufficient conditions for the boundedness of the anisotropic fractional maximal operator M d α in total anisotropic Morrey spaces L d p,λ,µ (R n).
Azerbaijan journal of mathematics, 2024
We establish a global generalized weighted Sobolev-Morrey W 1 M p,ϕ w-regularity for solutions to... more We establish a global generalized weighted Sobolev-Morrey W 1 M p,ϕ w-regularity for solutions to variational inequalities and obstacle problems for divergence form elliptic systems with measurable coefficients in bounded non-smooth domains.
Commutators of fractional maximal operator in variable Lebesgue spaces over bounded quasi‐metric measure spaces
Mathematical Methods in The Applied Sciences, Apr 22, 2022
Journal of Mathematical Inequalities, 2022
In this paper we introduce a new variant of Morrey spaces called total Morrey spaces L p,λ ,μ (R ... more In this paper we introduce a new variant of Morrey spaces called total Morrey spaces L p,λ ,μ (R n). These spaces generalize the classical Morrey spaces so that L p,λ ,λ (R n) ≡ L p,λ (R n) and the modified Morrey spaces so that L p,λ ,0 (R n) = L p,λ (R n). We give basic properties of the spaces L p,λ ,λ (R n) and study some embeddings into the Morrey space L p,λ ,μ (R n). We also give necessary and sufficient conditions for the boundedness of the maximal commutator operator M b and commutator of maximal operator [b,M] on L p,λ ,μ (R n). We obtain some new characterizations for certain subclasses of BMO(R n) .
arXiv (Cornell University), Dec 10, 2018
In the present paper, we will characterize the boundedness of the generalized fractional integral... more In the present paper, we will characterize the boundedness of the generalized fractional integral operators I ρ and the generalized fractional maximal operators M ρ on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators M ρ and I ρ on generalized Orlicz-Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators M ρ and I ρ on generalized Orlicz-Morrey spaces.
Journal of Mathematical Analysis and Applications, May 1, 2009
In this paper we obtain necessary and sufficient conditions on the parameters for the boundedness... more In this paper we obtain necessary and sufficient conditions on the parameters for the boundedness of the Dunkl-type fractional maximal operator M β , and the Dunkl-type fractional integral operator I β from the spaces L p,α (R) to the spaces L q,α (R), 1 < p < q < ∞, and from the spaces L 1,α (R) to the weak spaces WL q,α (R), 1 < q < ∞. In the case p = 2α+2 β , we prove that the operator M β is bounded from the space L p,α (R) to the space L ∞,α (R), and the Dunkl-type modified fractional integral operator I β is bounded from the space L p,α (R) to the Dunkl-type BMO space BMO α (R). By this results we get boundedness of the operators M β and I β from the Dunkl-type Besov spaces B s pθ,α
Journal of Mathematical Inequalities, 2021
We obtain the generalized Sobolev-Morrey spaces W 1 p,ϕ (Ω) estimate for weak solutions of a boun... more We obtain the generalized Sobolev-Morrey spaces W 1 p,ϕ (Ω) estimate for weak solutions of a boundary value problem for nonlinear elliptic equations with BMO coefficients in nonsmooth domains. We investigate regularity of the weak solutions in generalized Morrey spaces M p,ϕ (Ω). The nonlinearity has sufficiently small BMO seminorm and the boundary of the domain is sufficiently flat.
Advances in analysis, Jul 26, 2017
In this paper we consider some problems of the theory of approximation of functions on interval [... more In this paper we consider some problems of the theory of approximation of functions on interval [0, ∞) in the metric of L p,λ with weight sh 2λ x using generalized Gegenbauer shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Gegenbauer shifts. We establish the equivalence of the modulus of smoothness and K-functional, defined in terms of the space of the Sobolev type corresponding to the Gegenbauer differential operator. We define function spaces of Nikol'skii-Besov type and describe them in terms of best approximations. As a tool for approximation, we use some functions classes of spectrum. In these classes, we prove analogues of Bernstein's inequality and others for the Gegenbauer differential operator. Our results are analogues of the results for generalized Bessel shifts obtained in the work [30].
Advances in Nonlinear Analysis, 2023
In this article, we show continuity of commutators of Calderón-Zygmund operators [ ] b T , with B... more In this article, we show continuity of commutators of Calderón-Zygmund operators [ ] b T , with BMO functions in generalized Orlicz-Morrey spaces () M φ n Φ,. We give necessary and sufficient conditions for the boundedness of the genuine Calderón-Zygmund operators T and for their commutators [ ] b T , on generalized Orlicz-Morrey spaces, respectively.
arXiv (Cornell University), Apr 23, 2018
In this paper, we investigate the boundedness of maximal operator and its commutators in generali... more In this paper, we investigate the boundedness of maximal operator and its commutators in generalized Orlicz-Morrey spaces on the spaces of homogeneous type. As an application of this boundedness, we give necessary and sufficient condition for the Adams type boundedness of fractional integral and its commutators in these spaces. We also discuss criteria for the boundedness of these operators in Orlicz spaces.
Boundary Value Problems, Aug 21, 2017
Let L =-+ V be a Schrödinger operator, where is the Laplacian on R n and the non-negative potenti... more Let L =-+ V be a Schrödinger operator, where is the Laplacian on R n and the non-negative potential V belongs to the reverse Hölder class RH q for q ≥ n/2. In this paper, we study the boundedness of the Marcinkiewicz integral operators μ L j and their commutators [b, μ L j ] with b ∈ BMO θ (ρ) on generalized Morrey spaces M α,V p,ϕ (R n) associated with Schrödinger operator and vanishing generalized Morrey spaces VM α,V p,ϕ (R n) associated with Schrödinger operator. We find the sufficient conditions on the pair (ϕ 1 , ϕ 2) which ensure the boundedness of the operators μ L j from one vanishing generalized Morrey space VM α,V p,ϕ 1 to another VM α,V p,ϕ 2 , 1 < p < ∞ and from the space VM α,V 1,ϕ 1 to the weak space VWM α,V 1,ϕ 2. When b belongs to BMO θ (ρ) and (ϕ 1 , ϕ 2) satisfies some conditions, we also show that [b, μ L j ] is bounded from M α,V p,ϕ 1 to M α,V p,ϕ 2 and from VM α,V p,ϕ 1 to VM α,V p,ϕ 2 , 1 < p < ∞. MSC: 42B35; 35J10
Some Characterizations of BMO Spaces via Commutators in Orlicz Spaces on Stratified Lie Groups
Results in Mathematics, Dec 30, 2021
arXiv (Cornell University), May 23, 2014
arXiv (Cornell University), Jul 20, 2022
We give necessary and sufficient conditions for the boundedness of the maximal commutators M b , ... more We give necessary and sufficient conditions for the boundedness of the maximal commutators M b , the commutators of the maximal operator [b, M ] and the commutators of the sharp maximal operator [b, M ♯ ] in Orlicz spaces L Φ (G) on any stratified Lie group G when b belongs to Lipschitz spacesΛ β (G). We obtain some new characterizations for certain subclasses of Lipschitz spacesΛ β (G).
Complex Analysis and Operator Theory, Jul 26, 2014
We consider generalized Orlicz-Morrey spaces M Φ,ϕ (R n) including their weak versions W M Φ,ϕ (R... more We consider generalized Orlicz-Morrey spaces M Φ,ϕ (R n) including their weak versions W M Φ,ϕ (R n). We find the sufficient conditions on the pairs (ϕ 1 , ϕ 2) and (Φ, Ψ) which ensures the boundedness of the fractional maximal operator M α from M Φ,ϕ 1 (R n) to M Ψ,ϕ 2 (R n) and from M Φ,ϕ 1 (R n) to W M Ψ,ϕ 2 (R n). As applications of those results, the boundedness of the commutators of the fractional maximal operator M b,α with b ∈ BM O(R n) on the spaces M Φ,ϕ (R n) is also obtained. In all the cases the conditions for the boundedness are given in terms of supremal-type inequalities on weights ϕ(x, r), which do not assume any assumption on monotonicity of ϕ(x, r) on r.
arXiv (Cornell University), Nov 24, 2013
We study the boundedness of intrinsic square functions and their commutators on generalized Orlic... more We study the boundedness of intrinsic square functions and their commutators on generalized Orlicz-Morrey spaces M Φ,ϕ (R n). In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on weights ϕ(x, r) without assuming any monotonicity property of ϕ(x, r) on r.
Czechoslovak Mathematical Journal, Jun 1, 2014
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
Commutators of multilinear Calderón–Zygmund operators with kernels of Dini’s type on generalized weighted Morrey spaces and applications
Positivity, Dec 28, 2022
arXiv (Cornell University), Oct 24, 2013
We consider generalized Orlicz-Morrey spaces M Φ,ϕ (R n) including their weak versions W M Φ,ϕ (R... more We consider generalized Orlicz-Morrey spaces M Φ,ϕ (R n) including their weak versions W M Φ,ϕ (R n). In these spaces we prove the boundedness of the Riesz potential from M Φ,ϕ 1 (R n) to M Ψ,ϕ 2 (R n) and from M Φ,ϕ 1 (R n) to W M Ψ,ϕ 2 (R n). As applications of those results, the boundedness of the commutators of the Riesz potential on generalized Orlicz-Morrey space is also obtained. In all the cases the conditions for the boundedness are given either in terms of Zygmund-type integral inequalities on (ϕ 1 , ϕ 2), which do not assume any assumption on monotonicity of ϕ 1 (x, r), ϕ 2 (x, r) in r.
Carpathian Mathematical Publications, Dec 29, 2021
In this paper we investigate the best approximation by trigonometric polynomials in the variable ... more In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces M p(•),λ(•) (I 0 , w), where w is a weight function in the Muckenhoupt A p(•) (I 0) class. We get a characterization of K-functionals in terms of the modulus of smoothness in the spaces M p(•),λ(•) (I 0 , w). Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces M p(•),λ(•) (I 0 , w), the closure of the set of all trigonometric polynomials in M p(•),λ(•) (I 0 , w).
Uploads
Papers by Vagif S. Guliyev