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Mathematics Subject Classification: 44A05, 44A35With the help of a generalized convolution and prove Watson’s and Plancherel’s theorems. Using generalized convolutions a class of Toeplitz plus Hankel integral equations, and also a system of integro-differential equations are solved in closed form.

Generalized convolutions IV

K. Urbanik (1986)

Studia Mathematica

Global And Local Saturated Theorems In Some Spaces Of Temperate Functions

Tatjana Ostrogorski (1979)

Publications de l'Institut Mathématique

Global and local saturation theorems in some spaces of temperate functions.

T. Ostrogorski (1979)

Publications de l'Institut Mathématique [Elektronische Ressource]

Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

Gasmi, A., Sifi, M., Soltani, F. (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35We introduce some new weighted Herz spaces associated with the Dunkl operator on R. Also we characterize by atomic decompositions the corresponding Herz-type Hardy spaces. As applications we investigate the Dunkl transform on these spaces and establish a version of Hardy inequality for this transform.* The authors are supported by the DGRST research project 04/UR/15-02.

Homomorphismes discontinus des algèbres de Banach commutatives séparables

J. Esterle (1979)

Studia Mathematica

Integral transforms of the Kontorovich-Lebedev convolution type.

Semyon B. Yakubovich (2003)

Collectanea Mathematica

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]

Inversion of the dual Dunkl-Sonine transform on $ℝ$ using Dunkl wavelets.

Mourou, Mohamed Ali (2009)

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

Konstruktion von Operatoren und Kernen mit Hilfe von Absorptionsmengen.

G. Ritter (1975)

Mathematische Annalen

$L^{p}$ -improving properties of measures supported on curves on the Heisenberg group. II

Silvia Secco (2002)

Bollettino dell'Unione Matematica Italiana

$L^{p}$ - $L^{q}$ estimates are obtained for convolution operators by finite measures supported on curves in the Heisenberg group whose tangent vector at the origin is parallel to the centre of the group.

$L^{p} - L^{q}$ boundedness of analytic families of fractional integrals

Valentina Casarino, Silvia Secco (2008)

Studia Mathematica

We consider a double analytic family of fractional integrals $S_{z}^{γ, α}$ along the curve ${t \mapsto | t |}^{α}$ , introduced for α = 2 by L. Grafakos in 1993 and defined by $(S_{z}^{γ, α} f) (x ₁, x ₂) : = 1 / Γ (z + 1 / 2) {\int \int | u - 1 |}^{z} ψ (u - 1) {f (x ₁ - t, x ₂ - u | t |}^{α} {) d u | t |}^{γ} d t / t$ , where ψ is a bump function on ℝ supported near the origin, $f \in_{c}^{\infty} (ℝ ²)$ , z,γ ∈ ℂ, Re γ ≥ 0, α ∈ ℝ, α ≥ 2. We determine the set of all (1/p,1/q,Re z) such that $S_{z}^{γ, α}$ maps $L^{p} (ℝ ²)$ to $L^{q} (ℝ ²)$ boundedly. Our proof is based on product-type kernel arguments. More precisely, we prove that the kernel $K_{- 1 + i θ}^{i ϱ, α}$ is a product kernel on ℝ², adapted to the curve ${t \mapsto | t |}^{α}$ ; as a consequence, we show that the operator...

Linear operators and operational calculus, Part II

Harris Shultz (1972)

Studia Mathematica

Local convergence of convolution integral

Jörgen Löfström (1976)

Studia Mathematica

Lp-Improving Properties for Some Measures Supported on Curves.

Yibiao Pan (1996)

Mathematica Scandinavica

Mean-Periodic Functions Associated with the Jacobi-Dunkl Operator on R

Ben Salem, N., Ould Ahmed Salem, A., Selmi, B. (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 34K99, 44A15, 44A35, 42A75, 42A63Using a convolution structure on the real line associated with the Jacobi-Dunkl differential-difference operator Λα,β given by: Λα,βf(x) = f'(x) + ((2α + 1) coth x + (2β + 1) tanh x) { ( f(x) − f(−x) ) / 2 }, α ≥ β ≥ −1/2 , we define mean-periodic functions associated with Λα,β. We characterize these functions as an expansion series intervening appropriate elementary functions expressed in terms of the derivatives of the...

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