We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤ ∞,for which the potential operators are Lp—Lq bo...We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤ ∞,for which the potential operators are Lp—Lq bounded.This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions.We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers.展开更多
We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-PMey-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz trans...We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-PMey-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as, CalderSn-Zygmund operators for all possible values of type parameter λ, in this context. This extends results existing in the literature, but being justified only for a restricted range of λ.展开更多
The heat kernel in the setting of classical Fourier-Bessel expansions is defined by an os- cillatory series which cannot be computed explicitly. We prove qualitatively sharp estimates of this kernel. Our method relies...The heat kernel in the setting of classical Fourier-Bessel expansions is defined by an os- cillatory series which cannot be computed explicitly. We prove qualitatively sharp estimates of this kernel. Our method relies on establishing a connection with a situation of expansions based on Jacobi polynomials and then transferring known sharp bounds for the related Jacobi heat kernel.展开更多
The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of t...The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate.It follows that the solution converges to the solution of a nonlinear diffusion problem,as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.展开更多
基金supported by the National Science Centre of Poland within the project Opus 2013/09/B/ST1/02057
文摘We study potential operators and,more generally,Laplace-Stieltjes and Laplace type multipliers associated with the twisted Laplacian.We characterize those 1 ≤ p,q ≤ ∞,for which the potential operators are Lp—Lq bounded.This result is a sharp analogue of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the context of special Hermite expansions.We also investigate Lp mapping properties of the Laplace-Stieltjes and Laplace type multipliers.
基金supported by MTM2010/17974an FPU Grant from the Government of Spain
文摘We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-PMey-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as, CalderSn-Zygmund operators for all possible values of type parameter λ, in this context. This extends results existing in the literature, but being justified only for a restricted range of λ.
基金supported by MNiSW(Grant No.N201 417839)supported by(Grant No.MTM2012-36732-C03-02)from Spanish Government
文摘The heat kernel in the setting of classical Fourier-Bessel expansions is defined by an os- cillatory series which cannot be computed explicitly. We prove qualitatively sharp estimates of this kernel. Our method relies on establishing a connection with a situation of expansions based on Jacobi polynomials and then transferring known sharp bounds for the related Jacobi heat kernel.
基金supported by a Marie Curie Transfer of Knowledge Fellowship of the European Community’s Sixth Framework Programme(No. MTKD-CT-2004-013389)
文摘The authors consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction.It is deduced from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and satisfies estimates which do not depend on the kinetic rate.It follows that the solution converges to the solution of a nonlinear diffusion problem,as the size of the volume elements and the time steps converge to zero while the kinetic rate tends to infinity.
