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Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 5, Pages 957–974 (Mi izv1057)  

This article is cited in 3 scientific papers (total in 3 papers)

On the boundary behavior of functions in spaces of Hardy type

V. G. Krotov


Abstract: Let $X$ be a topological space with a measure $\mu$. In the product $\mathscr X=X\times (0,T]$ (or $\mathscr X=X\times [0,1)$) simple axioms are used to distinguish a family $\Gamma=\{\Gamma(x)\colon x\in X\}$ of domains for approaching the boundary of $\mathscr X$. Associated with the family $\Gamma$ is the maximal function
$$ \mathscr M_\Gamma u(x)=\sup \{|u(y,t)|\colon (y,t)\in\Gamma(x)\}. $$
The spaces $\mathscr H^p(\mathscr X,\Gamma,\mu)$ consisting of functions $u$ continuous on $\mathscr X$ with $\mathscr M_\Gamma u\in L^p$ are introduced, along with the subspaces of them consisting of the functions having a $\Gamma$-limit a.e. The properties of the spaces $\mathscr H^p$ and the action in them of operators of smoothing type are studied. The results are applied to Hardy spaces of harmonic or holomorphic functions.

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English version:
Mathematics of the USSR-Izvestiya, 1991, 37:2, 303–320

Bibliographic databases:

UDC: 517.51+517.56
MSC: Primary 30D40, 42B30; Secondary 30D55, 46J15
Received: 25.02.1987
Revised: 13.11.1989

Citation: V. G. Krotov, “On the boundary behavior of functions in spaces of Hardy type”, Izv. Akad. Nauk SSSR Ser. Mat., 54:5 (1990), 957–974; Math. USSR-Izv., 37:2 (1991), 303–320

Citation in format AMSBIB
\Bibitem{Kro90}
\by V.~G.~Krotov
\paper On~the boundary behavior of functions in spaces of Hardy type
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1990
\vol 54
\issue 5
\pages 957--974
\mathnet{http://mi.mathnet.ru/izv1057}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1086081}
\zmath{https://zbmath.org/?q=an:0733.46029|0713.46036}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..37..303K}
\transl
\jour Math. USSR-Izv.
\yr 1991
\vol 37
\issue 2
\pages 303--320
\crossref{https://doi.org/10.1070/IM1991v037n02ABEH002065}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. G. Krotov, “An exact estimate of the boundary behavior of functions from Hardy–Sobolev classes in the critical case”, Math. Notes, 62:4 (1997), 439–448  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. G. Krotov, “Tangential boundary behavior of functions of several variables”, Math. Notes, 68:2 (2000), 201–216  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Russian Math. (Iz. VUZ), 50:8 (2006), 59–64  mathnet  mathscinet  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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