Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Spline wavelet bases of weighted $ L\sp p$ spaces, $ 1\leq p<\infty$

Authors: J. García-Cuerva and K. S. Kazarian
Journal: Proc. Amer. Math. Soc. 123 (1995), 433-439
MSC: Primary 42C15; Secondary 46E30
MathSciNet review: 1216812
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study necessary conditions on the weight w for the spline wavelet systems to be bases in the weighted space $ {L^p}(w)$.

References [Enhancements On Off] (What's this?)

  • [Ch] C. K. Chui, An introduction to wavelets, Academic Press, New York, 1992. MR 1150048 (93f:42055)
  • [Ch-W] C. K. Chui and J. Z. Wang, On compactly supported spline wavelets and a duality principle, Trans. Amer. Math. Soc. 330 (1992), 903-915. MR 1076613 (92f:41020)
  • [C-D] Z. Cisielski and J. Domsta, Construction of an orthonormal basis in $ {C^m}({I^d})$ and $ W_p^m({I^d})$, Studia Math. 61 (1972), 210-223.
  • [D] G. David, Wavelets and singular integrals on curves and surfaces, Lecture Notes in Math., vol. 1465, Springer-Verlag, New York, 1991. MR 1123480 (92k:42021)
  • [G-K] J. García-Cuerva and K. S. Kazarian, Calderón-Zygmund Operators and unconditional bases of weighted Hardy spaces, Studia Math. 109 (1994), 255-276. MR 1274012 (95g:42024)
  • [G-R] J. García-Cuerva and José-Luis Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Math Stud., vol. 114, North-Holland, Amsterdam, 1985. MR 807149 (87d:42023)
  • [K] K. S. Kazarian, On the multiplicative completion of some orthonormal systems to bases in $ {L^p},1 \leq p < \infty $, Anal. Math. 4 (1978), 37-52. (Russian) MR 0481910 (58:2001)
  • [K2] -, On bases and unconditional bases in the spaces $ {L^p}(d\mu ),1 \leq p < \infty $, Studia Math. 71 (1982), 227-249.
  • [M] Y. Meyer, Ondelettes el opérateurs, vols. I and II, Hermann, Paris, 1990. MR 1085487 (93i:42002)
  • [Mu] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. MR 0293384 (45:2461)
  • [S] J.-O. Strömberg, A modified Franklin system and higher order spline systems on $ {R^n}$ as unconditional bases for Hardy spaces, Proc. Conf. in Honor of Antoni Zygmund (W. Beckner, A. P. Calderón, R. Fefferman, and P. W. Jones, eds.), Wadsworth, New York, 1981, pp. 475-493. MR 730086 (85d:42027)
  • [Z] R. E. Zink, The Franklin system as Schauder basis for $ L_\mu ^p[0,1]$, Proc. Amer. Math. Soc. 103 (1988), 225-233. MR 938673 (89d:46035)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42C15, 46E30

Retrieve articles in all journals with MSC: 42C15, 46E30

Additional Information

Keywords: Wavelets, splines, $ {A_p}$ weights, Schauder, unconditional bases
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society