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E. Dolzhenko
E. Dolzhenko
тВЕННыИ УНИВЕРс ИтЕтИМЕНИ М. В. лОМОНОс ОВА МЕхАНИкО-МАтЕМАт ИЧЕскИИ ФАкУльтЕт МОскОВскИИ гОсУ ДАРс 17 234 Mockba CCCP 17 234 Mockba CCCP
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Kh. Makhmudov
Kh. Makhmudov
тВЕННыИ УНИВЕРс ИтЕтИМЕНИ М. В. лОМОНОс ОВА МЕхАНИкО-МАтЕМАт ИЧЕскИИ ФАкУльтЕт МОскОВскИИ гОсУ ДАРс 17 234 Mockba CCCP 17 234 Mockba CCCP
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Abstract
пУстьE — ИжМЕРИМОЕ пО лЕБЕгУ ОгРАНИЧЕННОЕ МНОжЕстВО пОлОжИтЕльНОИ плОЩА ДИ mes2E кОМплЕксНОИ плОск ОстИ с. кАк ОБыЧНО, пРИp≧1 ОБОжНАЧИМ ЧЕРЕжLp(E) БА НАхОВО пРОстРАНстВО ИжМЕРИ Мых пО лЕБЕгУ НАE кОМплЕксНОжНАЧНых Ф УНкцИИf с сУММИРУЕМО Иp—стЕпЕНьУ Их МОДУль И ОБыЧНОИ НОРМОИ
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$$\left\| \cdot \right\|_p = \left\| \cdot \right\|_{L_p (E)}$$
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. ЧЕР ЕжLpRn(f,E) ОБОжНАЧИМ НАИМЕН ьшЕЕ УклОНЕНИЕf∃Lp(E) От РАц ИОНАльНых ФУНкцИИ ст ЕпЕНИ ≦n кОМплЕксНОгО пЕРЕМЕ ННОгОz пО НОРМЕ ∥ ∥. пОлОжИМf(z)=0 Дльz∃CE,Eδ —δ-ОкРЕстНОсть МНО жЕстВАE (δ>0), И\documentclass{aastex}
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$$\omega _p (\delta ,f) = \mathop {\sup {\mathbf{ }}}\limits_{\left| h \right|< \delta } \{ \int\limits_{E_\sigma } {\int {{\mathbf{ }}|f(z + h) - f(z)|^p } d\sigma } \} ^{1/p} .$$
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$$\begin{array}{*{20}c} {L^p R_n (f,E) \leqq 12\omega _p \left( {\frac{{\delta + \ln n}}{{\sqrt n }},f} \right){\mathbf{ }}npu{\mathbf{ }}p = 1,} \\ {L^p R_n (f,E) \leqq \frac{{24}}{{(p - 1)(2 - p)}}\omega _p (n^{(p - 2)/2p} ,f){\mathbf{ }}npu{\mathbf{ }}1< p< 2,} \\ {L^1 R_n (\bar z,[0,1] \times [0,1]) \geqq \frac{1}{{32\sqrt n }}.} \\ \end{array}$$
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| Analysis Mathematica | |
|---|---|
| Language | English |
| Size | B5 |
| Year of Foundation |
1975 |
| Volumes per Year |
1 |
| Issues per Year |
4 |
| Founder | Akadémiai Kiadó |
| Founder's Address |
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245 |
| Publisher | Akadémiai Kiadó Springer Nature Switzerland AG |
| Publisher's Address |
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11. |
| Responsible Publisher |
Chief Executive Officer, Akadémiai Kiadó |
| ISSN | 0133-3852 (Print) |
| ISSN | 1588-273X (Online) |
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