Geodesic
Commutators and Analytic Dependence of Fourier-Bessel Series on (0, ∞)
Canadian mathematical bulletin, Tome 42 (1999) no. 2, pp. 198-208

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we study the boundedness of the commutators $[b,\,{{S}_{n}}]$ where $b$ is a $\text{BMO}$ function and ${{S}_{n}}$ denotes the $n$ -th partial sum of the Fourier-Bessel series on $(0,\,\infty )$ . Perturbing the measure by $\text{exp(}2\text{b)}$ we obtain that certain operators related to ${{S}_{n}}$ depend analytically on the functional parameter $b$ .
DOI : 10.4153/CMB-1999-024-1
Mots-clés : 42C10, Fourier-Bessel series, commutators, BMO, Ap weights 
Guadalupe, José J.; Pérez, Mario; Varona, Juan L. Commutators and Analytic Dependence of Fourier-Bessel Series on (0, ∞). Canadian mathematical bulletin, Tome 42 (1999) no. 2, pp. 198-208. doi: 10.4153/CMB-1999-024-1
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[1] [1] Aptekarev, A. I., Branquinho, A. and Marcellán, F., Toda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation. J. Comput. Appl. Math. 78 (1997), 139–160. Google Scholar

[2] [2] Bloom, S., A commutator theorem and weighted BMO. Trans. Amer. Math. Soc. 292 (1985), 103–122. Google Scholar

[3] [3] Coifman, R. R. and Murray, M. A. M., Uniform analyticity of orthogonal projections. Trans. Amer.Math. Soc. 312 (1989), 779–817. Google Scholar

[4] [4] Coifman, R. R., Rochberg, R. and Weiss, G., Factorization theorems for Hardy spaces in several variables. Ann. of Math. 103 (1976), 611–635. Google Scholar

[5] [5] Còrdoba, A., The disc multiplier. Duke Math. J. 58 (1989), 21–29. Google Scholar

[6] [6] Garcìa-Cuerva, J. and de Francia, J. L. Rubio, Weighted norm inequalities and related topics. North-Holland, Amsterdam, 1985. Google Scholar

[7] [7] Marcellán, F., Dehesa, J. S. and Ronveaux, A., On orthogonal polynomials with perturbed recurrence relations. J. Comput. Appl. Math. 30 (1990), 203–212. Google Scholar

[8] [8] Neugebauer, C. J., Inserting Ap weights. Proc. Amer. Math. Soc. 87 (1983), 644–648. Google Scholar

[9] [9] Nevai, P. and Van Assche, W., Compact perturbations of orthogonal polynomials. Pacific J. Math. 153 (1992), 163–184. Google Scholar

[10] [10] Segovia, C. and Torrea, J. L., Vector-valued commutators and applications. Indiana Univ. Math. J. 38 (1989), 959–971. Google Scholar

[11] [11] Segovia, C. and Torrea, J. L., Weighted inequalities for commutators of fractional and singular integrals. Publ.Mat. 35 (1991), 209–235. Google Scholar

[12] [12] Segovia, C. and Torrea, J. L., Higher order commutators for vector-valued Calderòn-Zygmund operators. Trans. Amer.Math. Soc. 336 (1993), 537–556. Google Scholar

[13] [13] Varona, J. L., Fourier series of functions whose Hankel transform is supported on [0, 1]. Constr. Approx. 10 (1994), 65–75. Google Scholar

[14] [14] Watson, G. N., A treatise on the theory of Bessel functions. 2nd edn, Cambridge University Press, Cambridge, 1944 (reprinted 1995). Google Scholar

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