Riesz transforms for Dunkl transform

Bechir Amri; Mohamed Sifi

Displaying similar documents to “Riesz transforms for Dunkl transform”

Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

Guliyev, Vagif, Hasanov, Javanshir (2006)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 42B20, 42B25, 42B35 We consider the generalized shift operator, generated by the Laplace- Bessel differential operator [...] The Bn -maximal functions and the Bn - Riesz potentials, generated by the Laplace-Bessel differential operator ∆Bn are investigated. We study the Bn - Riesz potentials in the Bn - Morrey spaces and Bn - BMO spaces. An inequality of Sobolev - Morrey type is established for the Bn - Riesz potentials. ...

The Stein-Weiss Type Inequality for Fractional Integrals, Associated with the Laplace-Bessel Differential Operator

Gadjiev, Akif, Guliyev, Vagif (2008)

Fractional Calculus and Applied Analysis

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2000 Math. Subject Classification: Primary 42B20, 42B25, 42B35 In this paper we study the Riesz potentials (B -Riesz potentials) generated by the Laplace-Bessel differential operator ∆B. * Akif Gadjiev’s research is partially supported by the grant of INTAS (project 06-1000017-8792) and Vagif Guliyev’s research is partially supported by the grant of the Azerbaijan–U.S. Bilateral Grants Program II (project ANSF Award / 16071) and by the grant of INTAS (project...

On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

Abdelkefi, Chokri, Sifi, Mohamed (2006)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 44A15, 44A35, 46E30 In this paper we prove that the partial Dunkl integral ST(f) of f converges to f, as T → +∞ in L^∞(νµ) and we show that the Dunkl transform Fµ(f) of f is in L^1(νµ) when f belongs to a suitable Besov-Dunkl space. We also give sufficient conditions on a function f in order that the Dunkl transform Fµ(f) of f is in a L^p -space. * Supported by 04/UR/15-02.

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mejjaoli, Hatem (2006)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: Primary 35R10, Secondary 44A15 We establish an analogue of Beurling-Hörmander’s theorem for the Dunkl-Bessel transform FD,B on R(d+1,+). We deduce an analogue of Gelfand-Shilov, Hardy, Cowling-Price and Morgan theorems on R(d+1,+) by using the heat kernel associated to the Dunkl-Bessel-Laplace operator.

Besov-type spaces on R $d$ and integrability for the Dunkl transform.

Abdelkefi, Chokri, Anker, Jean-Philippe, Sassi, Feriel, Sifi, Mohamed (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Sonine transform associated to the Dunkl kernel on the real line.

Soltani, Fethi (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Spectrum of Functions for the Dunkl Transform on R^d

Mejjaoli, Hatem, Trimèche, Khalifa (2007)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 42B10 In this paper, we establish real Paley-Wiener theorems for the Dunkl transform on R^d. More precisely, we characterize the functions in the Schwartz space S(R^d) and in L^2k(R^d) whose Dunkl transform has bounded, unbounded, convex and nonconvex support.

The size of $(L^{2}, L^{p})$ multipliers

Kathryn Hare (1992)

Colloquium Mathematicae

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Inversion formulas for the Dunkl intertwining operator and its dual on spaces of functions and distributions.

Trimèche, Khalifa (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Almost Everywhere Convergence of Riesz-Raikov Series

Ai Fan (1995)

Colloquium Mathematicae

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Let T be a d×d matrix with integer entries and with eigenvalues >1 in modulus. Let f be a lipschitzian function of positive order. We prove that the series $\sum_{n = 1}^{\infty} c_{n} f (T^{n} x)$ converges almost everywhere with respect to Lebesgue measure provided that $\sum_{n = 1}^{\infty} {| c_{n} |}^{2} l o g^{2} n < \infty$ .