Equivalence of the Haar and Franklin systems in certain function spaces

A. A. Komissarov

doi:10.1007/bf00971286

journal article Sep 01, 1982

Equivalence of the Haar and Franklin systems in certain function spaces

A. A. Komissarov

Siberian Mathematical Journal Vol. 23 No. 5 pp. 681-690 · Springer Science and Business Media LLC

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References

11

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S. Kaczmarz and H. Steinhaus, Orthogonal Series, Chelsea Publishing.

[2]

Z. Ciesielski, “Properties of the orthonormal Franklin system,” Stud. Math.,23, No. 2, 141–157 (1963). 10.4064/sm-23-2-141-157

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Z. Ciesielski, P. Simon, and P. Sjölin, “Equivalence of Haar and Franklin bases in Lp spaces,” Stud. Math.,60, No. 2, 195–211 (1976). 10.4064/sm-60-2-195-210

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P. Sjölin, “The Haar and Franklin systems are not equivalent bases in Ll,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,25, No. 11, 1099–1100 (1977).

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R. Ryan, “Conjugate functions in Orlicz spaces,” Pac. J. Math.,13, No. 4, 1371–1377 (1963). 10.2140/pjm.1963.13.1371

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Z. Ciesielski, “Properties of the orthonormal Franklin system. II,” Stud. Math.,27, No. 3, 289–323 (1966). 10.4064/sm-27-3-289-323

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A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Graylock (1961).

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M. A. Krasnosel'skii and Ya. B. Rutitskii, Convex Functions and Orlicz Spaces [in Russian], Fizmatgiz, Moscow (1958).

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A. Zygmund, Trigonometrical Series, Cambridge Univ. Press (1968).

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S. Lozinski, “On convergence and summability of Fourier series and interpolation processes,” Mat. Sb.,14, No. 3, 175–268 (1944).

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Z. Ciesielski and S. Kwapien, “Some properties of the Haar, Walsh-Paley, Franklin and the bounded polygonal orthonormal basis in Lp spaces,” Comment. Mathematicae, Tomus Specialis in Honorem Ladisllai Orlicz, Part 2, 37–42, Warsaw (1979).

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Published: Sep 01, 1982
Vol/Issue: 23(5)
Pages: 681-690
License: View

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A. A. Komissarov

Cite This Article

A. A. Komissarov (1982). Equivalence of the Haar and Franklin systems in certain function spaces. Siberian Mathematical Journal, 23(5), 681-690. https://doi.org/10.1007/bf00971286

Equivalence of the Haar and Franklin systems in certain function spaces

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