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Mat. Sb., 1998, Volume 189, Number 2, Pages 3–72 (Mi msb290)  

This article is cited in 5 scientific papers (total in 5 papers)

Maximization of functionals in $H^\omega [a,b]$

S. K. Bagdasarov

Ohio State University

Abstract: The structure and the properties of the extremal functions in the problem
$$ \int _a^b h(t)\psi (t) dt\to \sup, \qquad h\in H^\omega [a,b], $$
are described in the case when $\psi$ is an integrable function with zero mean and finitely many points of sign change on $[a,b]$ and $H^\omega [a,b]$ is the class of absolutely integrable functions on $[a,b]$ with modulus of continuity majorized by a fixed convex modulus of continuity $\omega$.

DOI: https://doi.org/10.4213/sm290

Full text: PDF file (782 kB)
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English version:
Sbornik: Mathematics, 1998, 189:2, 159–226

Bibliographic databases:

UDC: 517.988
MSC: Primary 41A17, 41A46, 41A50; Secondary 46E35
Received: 27.05.1996 and 02.10.1997

Citation: S. K. Bagdasarov, “Maximization of functionals in $H^\omega [a,b]$”, Mat. Sb., 189:2 (1998), 3–72; Sb. Math., 189:2 (1998), 159–226

Citation in format AMSBIB
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\by S.~K.~Bagdasarov
\paper Maximization of functionals in $H^\omega [a,b]$
\jour Mat. Sb.
\yr 1998
\vol 189
\issue 2
\pages 3--72
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\transl
\jour Sb. Math.
\yr 1998
\vol 189
\issue 2
\pages 159--226
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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. S. K. Bagdasarov, “Properties of $\omega$-Rearrangements”, Funct. Anal. Appl., 33:3 (1999), 161–177  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. S. K. Bagdasarov, “Extremal functions of integral functionals in $H^\omega[a,b]$”, Izv. Math., 63:3 (1999), 425–480  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Bagdasarov S.K., “Extremal problems in generalized Sobolev classes”, Analysis of Divergence: Control and Management of Divergent Processes, Applied and Numerical Harmonic Analysis, 1999, 327–357  mathscinet  zmath  isi
    4. Bagdasarov, SK, “Generalizations of the time optimal problem and Lyapunov theorem on the range of vector measures”, Journal of Approximation Theory, 147:1 (2007), 81  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. S. K. Bagdasarov, “Kolmogorov inequalities for functions in classes $W^rH^\omega$ with bounded $\mathbb L_p$-norm”, Izv. Math., 74:2 (2010), 219–279  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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