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On Hartman almost periodic functions

Guy Cohen, Viktor Losert (2006)

Studia Mathematica

We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in d or d . We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally compact, abelian groups are considered. We define generalized Marcinkiewicz spaces based upon arbitrary measure spaces...

On Limiting Case of the Stein-Weiss Type Inequality for the B-Riesz Potentials

Guliyev, Emin (2009)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: Primary 42B20, 42B25, 42B35In this paper we study the Riesz potentials (B-Riesz potentials) generated by the Laplace-Bessel differential operator ∆B [...]. We establish an inequality of Stein-Weiss type for the B-Riesz potentials in the limiting case, and obtain the boundedness of the B-Riesz potential operator from the space Lp,|x|β,γ to BMO|x|−λ,γ.* Emin Guliyev’s research partially supported by the grant of INTAS YS Collaborative Call with Azerbaijan 2005...

On Maximal Function on the Laguerre Hypergroup

Guliyev, Vagif, Assal, Miloud (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35Let K = [0, ∞)×R be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group. In this paper we consider the generalized shift operator, generated by Laguerre hypergroup, by means of which the maximal function is investigated. For 1 < p ≤ ∞ the Lp(K)-boundedness and weak L1(K)-boundedness result for the maximal function is obtained.* V. Guliyev partially supported by grant of INTAS...

On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols

Gladis Pradolini, Jorgelina Recchi (2023)

Czechoslovak Mathematical Journal

We prove two-weighted norm estimates for higher order commutator of singular integral and fractional type operators between weighted L p and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region out of which the classes of weights are satisfied by trivial weights. We also exhibit pairs of nontrivial...

On some subspaces of Morrey-Sobolev spaces and boundedness of Riesz integrals

Mouhamadou Dosso, Ibrahim Fofana, Moumine Sanogo (2013)

Annales Polonici Mathematici

For 1 ≤ q ≤ α ≤ p ≤ ∞, ( L q , l p ) α is a complex Banach space which is continuously included in the Wiener amalgam space ( L q , l p ) and contains the Lebesgue space L α . We study the closure ( L q , l p ) c , 0 α in ( L q , l p ) α of the space of test functions (infinitely differentiable and with compact support in d ) and obtain norm inequalities for Riesz potential operators and Riesz transforms in these spaces. We also introduce the Sobolev type space W ¹ ( ( L q , l p ) α ) (a subspace of a Morrey-Sobolev space, but a superspace of the classical Sobolev space W 1 , α ) and obtain...

On the boundary convergence of solutions to the Hermite-Schrödinger equation

Peter Sjögren, J. L. Torrea (2010)

Colloquium Mathematicae

In the half-space d × , consider the Hermite-Schrödinger equation i∂u/∂t = -Δu + |x|²u, with given boundary values on d . We prove a formula that links the solution of this problem to that of the classical Schrödinger equation. It shows that mixed norm estimates for the Hermite-Schrödinger equation can be obtained immediately from those known in the classical case. In one space dimension, we deduce sharp pointwise convergence results at the boundary by means of this link.

On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces

Ali Akbulut, Vagif Guliyev, Rza Mustafayev (2012)

Mathematica Bohemica

In the paper we find conditions on the pair ( ω 1 , ω 2 ) which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space p , ω 1 to another p , ω 2 , 1 < p < , and from the space 1 , ω 1 to the weak space W 1 , ω 2 . As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.

On the Hermite expansions of functions from the Hardy class

Rahul Garg, Sundaram Thangavelu (2010)

Studia Mathematica

Considering functions f on ℝⁿ for which both f and f̂ are bounded by the Gaussian e - 1 / 2 a | x | ² , 0 < a < 1, we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for O(n)-finite functions, thus extending a one-dimensional result of Vemuri.

On the range of the Fourier transform connected with Riemann-Liouville operator

Lakhdar Tannech Rachdi, Ahlem Rouz (2009)

Annales mathématiques Blaise Pascal

We characterize the range of some spaces of functions by the Fourier transform associated with the Riemann-Liouville operator α , α 0 and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schwartz theorems.

One-weight weak type estimates for fractional and singular integrals in grand Lebesgue spaces

Vakhtang Kokilashvili, Alexander Meskhi (2014)

Banach Center Publications

We investigate weak type estimates for maximal functions, fractional and singular integrals in grand Lebesgue spaces. In particular, we show that for the one-weight weak type inequality it is necessary and sufficient that a weight function belongs to the appropriate Muckenhoupt class. The same problem is discussed for strong maximal functions, potentials and singular integrals with product kernels.

Optimality of the range for which equivalence between certain measures of smoothness holds

Z. Ditzian (2010)

Studia Mathematica

Recently it was proved for 1 < p < ∞ that ω m ( f , t ) p , a modulus of smoothness on the unit sphere, and K ̃ ( f , t m ) p , a K-functional involving the Laplace-Beltrami operator, are equivalent. It will be shown that the range 1 < p < ∞ is optimal; that is, the equivalence ω m ( f , t ) p K ̃ ( f , t r ) p does not hold either for p = ∞ or for p = 1.

Orlicz bounds for operators of restricted weak type

Paul Alton Hagelstein (2005)

Colloquium Mathematicae

It is shown that if T is a sublinear translation invariant operator of restricted weak type (1,1) acting on L¹(𝕋), then T maps simple functions in L log L(𝕋) boundedly into L¹(𝕋).

Orlicz-Morrey spaces and the Hardy-Littlewood maximal function

Eiichi Nakai (2008)

Studia Mathematica

We prove basic properties of Orlicz-Morrey spaces and give a necessary and sufficient condition for boundedness of the Hardy-Littlewood maximal operator M from one Orlicz-Morrey space to another. For example, if f ∈ L(log L)(ℝⁿ), then Mf is in a (generalized) Morrey space (Example 5.1). As an application of boundedness of M, we prove the boundedness of generalized fractional integral operators, improving earlier results of the author.

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