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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 linear extension for interpolating sequences

Eric Amar (2008)

Studia Mathematica

Let A be a uniform algebra on X and σ a probability measure on X. We define the Hardy spaces H p ( σ ) and the H p ( σ ) interpolating sequences S in the p-spectrum ℳ p of σ. We prove, under some structural hypotheses on A and σ, that if S is a “dual bounded” Carleson sequence, then S is H s ( σ ) -interpolating with a linear extension operator for s < p, provided that either p = ∞ or p ≤ 2. In the case of the unit ball of ℂⁿ we find, for instance, that if S is dual bounded in H ∞ ( ) then S is H p ( ) -interpolating with a linear...

On local properties of functions and singular integrals in terms of the mean oscillation

Rahim Rzaev, Lala Aliyeva (2008)

Open Mathematics

This paper is devoted to research on local properties of functions and multidimensional singular integrals in terms of their mean oscillation. The conditions guaranteeing existence of a derivative in the L p-sense at a given point are found. Spaces which remain invariant under singular integral operators are considered.

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 maximal functions over circular sectors with rotation invariant measures

Hugo A. Aimar, Liliana Forzani, Virginia Naibo (2001)

Commentationes Mathematicae Universitatis Carolinae

Given a rotation invariant measure in ℝ n , we define the maximal operator over circular sectors. We prove that it is of strong type ( p , p ) for p > 1 and we give necessary and sufficient conditions on the measure for the weak type ( 1 , 1 ) inequality. Actually we work in a more general setting containing the above and other situations.

On maximal functions with rough kernels in L (log L)1/2(Sn-1).

Ahmad Al-Salman (2005)

Collectanea Mathematica

In this paper, we study the Lp mapping properties of maximal functions with rough kernels that are related to certain class of singular integral operators. We prove that our maximal functions are bounded on Lp provided that their kernels are in L (log L)1/2(Sn-1). Moreover, we present an example showing that our size condition on the kernel is optimal. As a consequence of our result, we substantially improve previously known results on maximal functions, singular integral operators, and Parametric...

On modular approximation property in the Besicovitch-Orlicz space of almost periodic functions

Mohamed Morsli (1997)

Commentationes Mathematicae Universitatis Carolinae

We investigate some convergence questions in the class of Besicovitch-Orlicz spaces of vector valued functions. Next, the existence problem of the projection operator on closed convex subsets is considered in the class of almost periodic functions. This problem was considered in [5], in the case of an Orlicz space. The approximation property obtained in both cases are of the same kind. However, the arguments which are used in the proofs are different.

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