Transplantation and Multiplier Theorems for Fourier-bessel Expansions
نویسنده
چکیده
Proved are weighted transplantation inequalities for Fourier-Bessel expansions. These extend known results on this subject by considering the largest possible range of parameters, allowing more weights and admitting a shift. The results are then used to produce a fairly general multiplier theorem with power weights for considered expansions. Also fractional integral results and conjugate function norm inequalities for these expansions are proved.
منابع مشابه
Properties of the Symbol of Multidimensional Singular Integrals in the Weighted Spaces and Oscillating Multipliers
Differential properties of symbols of multidimensional singular integrals in the weighted space of Bessel potentials on the sphere with the weighted functions, having singularities on a sphere are studied. The main results are applied to obtaining theorems on Fourier multipliers of spherical harmonic expansions.
متن کاملOPERATOR-VALUED Lq → Lp FOURIER MULTIPLIERS
Fourier multiplier theorems provides one of the most important tools in the study of partial differential equations and embedding theorems. They are very often used to establish maximal regularity of elliptic and parabolic differential operator equations. Operator–valued multiplier theorems in Banach–valued function spaces have been discussed extensively in [1, 2, 3, 5, 7, 8, 9, 10, 11, 12 ]. B...
متن کاملTransference Results for Multipliers, Maximal Multipliers and Transplantation Operators Associated with Fourier-bessel Expansions and Hankel Transform
Our objective in this survey is to present some results concerning to transference of multipliers, maximal multipliers and transplantation operators between Fourier-Bessel series and Hankel integrals. Also we list some related problems that can be interesting and that have not been studied yet. From August 31st to September 3rd, 2004, was held in Merlo (San Luis, Argentine) the congress ”VII En...
متن کاملPOINTWISE CONVERGENT EXPANSIONS IN q-FOURIER-BESSEL SERIES
Abstract: We define q-analogues of Fourier-Bessel series, by means of complete qorthogonal systems constructed with the third Jackson q-Bessel function. Sufficient conditions for pointwise convergence of these series are obtained, in terms of a general convergence principle valid for other Fourier series on grids defined over numerable sets. The results are illustrated with specific examples of...
متن کاملA Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions
A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order 0 as well as evaluating Schlömilch and Fourier–Bessel expansions in O(N(logN)2/ loglogN) operations. The algorithm is based on an asymptotic expansion for Bessel functions of large arguments, the fast Fourier transform, and the Neumann addition formula. All the algorithmic parameters are se...
متن کامل