RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (882 kB)
References: PDF file   HTML file

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
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} 

• http://mi.mathnet.ru/eng/izv1057
• http://mi.mathnet.ru/eng/izv/v54/i5/p957

 SHARE:

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. 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
2. V. G. Krotov, “Tangential boundary behavior of functions of several variables”, Math. Notes, 68:2 (2000), 201–216
3. Russian Math. (Iz. VUZ), 50:8 (2006), 59–64
•  Number of views: This page: 309 Full text: 94 References: 48 First page: 2