Representation of Functions in L1μ Weighted Spaces by Series with Monotone Coefficients in the Walsh Genrealized System

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References

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[5] M. G. Grigorian and Robert E.Zink,”Subsistems of the Walsh Orthogonal System Whose Multiplicative Completions Are Quasibases for 0 *L ^{p}_{[0.1]}*,1≤

http://dx.doi.org/10.1090/S0002-9939-02-06618-2

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[10] R. E. A. C. Paley, “A Remarkable Set of Orthogonal Functions,” Proceedings of the London Mathematical Society, Vol. 34, No. 1, 1932, pp. 241-279.

http://dx.doi.org/10.1112/plms/s2-34.1.241

[11] A. A. Talalian, “Representation of Measurable Functions by Series,” UMN, Vol. 15, No. 5, 1960, pp. 567-604.

[12] P. L. Ul’janov, “Representation of Functions by Series and Classes φ(L),” UMN, Vol. 25, No. 2, 1972, pp. 3-52.

[13] H. E. Chrestenson, “A Class of Generalized Walsh Functions,’’ Pacific Journal of Mathematics, Vol. 45, No. 1, 1955, pp. 17-31. http://dx.doi.org/10.2140/pjm.1955.5.17

[14] W. Young, “Mean Convergence of Generalized WalshFourier Series,” Transactions of the American Mathematical Society, Vol. 218, 1976, pp. 311-320.

http://dx.doi.org/10.1090/S0002-9947-1976-0394022-8