Exact Solutions of Nonlocal Pluriparabolic Problems
MSC 2010: 44A35, 44A40
Chobanov, Georgi, Dimovski, Ivan (2012)
Mathematica Balkanica New Series
MSC 2010: 44A35, 44A40
Diagana, Toka (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Norbert Ortner (1980)
Mathematische Annalen
Sonja Lyttkens (1974)
Mathematica Scandinavica
Xuan Thao, Nguyen, Kim Tuan, Vu, Thanh Hong, Nguyen (2008)
Fractional Calculus and Applied Analysis
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.
K. Urbanik (1986)
Studia Mathematica
Tatjana Ostrogorski (1979)
Publications de l'Institut Mathématique
T. Ostrogorski (1979)
Publications de l'Institut Mathématique [Elektronische Ressource]
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.
J. Esterle (1979)
Studia Mathematica
Semyon B. Yakubovich (2003)
Collectanea Mathematica
Trimèche, Khalifa (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Mourou, Mohamed Ali (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
G. Ritter (1975)
Mathematische Annalen
Silvia Secco (2002)
Bollettino dell'Unione Matematica Italiana
- 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.
Valentina Casarino, Silvia Secco (2008)
Studia Mathematica
We consider a double analytic family of fractional integrals along the curve , introduced for α = 2 by L. Grafakos in 1993 and defined by , where ψ is a bump function on ℝ supported near the origin, , z,γ ∈ ℂ, Re γ ≥ 0, α ∈ ℝ, α ≥ 2. We determine the set of all (1/p,1/q,Re z) such that maps to boundedly. Our proof is based on product-type kernel arguments. More precisely, we prove that the kernel is a product kernel on ℝ², adapted to the curve ; as a consequence, we show that the operator...
Harris Shultz (1972)
Studia Mathematica
Jörgen Löfström (1976)
Studia Mathematica
Yibiao Pan (1996)
Mathematica Scandinavica
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...