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Mat. Zametki, 2011, Volume 90, Issue 3, Pages 340–350 (Mi mz9222)  

This article is cited in 8 scientific papers (total in 8 papers)

On the Properties of the $Q$-Integral

M. P. Efimova

M. V. Lomonosov Moscow State University

Abstract: We study the Titchmarsh $Q$-integral, its generalization, and its elementary properties are studied; integrability criteria on sets of finite measure are obtained.

Keywords: $Q$-integral, $A$-integral, integrability criterion, Kurzweil–Henstock integral, Lebesgue criterion, Fourier series, conjugate trigonometric series

DOI: https://doi.org/10.4213/mzm9222

Full text: PDF file (462 kB)
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English version:
Mathematical Notes, 2011, 90:3, 322–332

Bibliographic databases:

UDC: 517.518.126
Received: 08.07.2010
Revised: 14.10.2010

Citation: M. P. Efimova, “On the Properties of the $Q$-Integral”, Mat. Zametki, 90:3 (2011), 340–350; Math. Notes, 90:3 (2011), 322–332

Citation in format AMSBIB
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\paper On the Properties of the $Q$-Integral
\jour Mat. Zametki
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\issue 3
\pages 340--350
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\jour Math. Notes
\yr 2011
\vol 90
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\pages 322--332
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. P. Efimova, “Dostatochnoe uslovie zameny peremennoi v obobschennom $q$-integrale”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 13:1(2) (2013), 43–46  mathnet
    2. R. A. Aliyev, “$N^\pm$-integrals and boundary values of Cauchy-type integrals of finite measures”, Sb. Math., 205:7 (2014), 913–935  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. M. P. Efimova, “The sufficient condition for integrability of a generalized $Q$-integral and points of integrability”, Moscow University Mathematics Bulletin, 70:4 (2015), 181–184  mathnet  crossref  mathscinet
    4. Aliev R.A., “On Properties of Hilbert Transform of Finite Complex Measures”, Complex Anal. Oper. Theory, 10:1 (2016), 171–185  crossref  mathscinet  zmath  isi  scopus
    5. Aliev R.A., “On Laurent Coefficients of Cauchy Type Integrals of Finite Complex Measures”, Proc. Inst. Math. Mech., 42:2 (2016), 292–303  mathscinet  zmath  isi
    6. Aliev R.A., “Riesz's Equality For the Hilbert Transform of the Finite Complex Measures”, Azerbaijan J. Math., 6:1 (2016), 126–135  mathscinet  zmath  isi  elib
    7. Aliev R.A., “Representability of Cauchy-type integrals of finite complex measures on the real axis in terms of their boundary values”, Complex Var. Elliptic Equ., 62:4 (2017), 536–553  crossref  mathscinet  zmath  isi  scopus
    8. Aliev R.A. Nebiyeva Kh. I., “The a-Integral and Restricted Ahlfors-Beurling Transform”, Integral Transform. Spec. Funct., 29:10 (2018), 820–830  crossref  mathscinet  zmath  isi  scopus
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