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О ДИФФЕРЕНцИРОВАНИИ ИНтЕгРАлОВ От ФУНкцИ И Иж сИММЕтРИЧНых пРОс тРАНстВ ДИФФЕРЕНцИАльНыМИ Б АжИсАМИ

On the differentiation of integrals of functions from symmetric spaces by differential bases

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Abstract

We consider new methods of constructing differential bases. Symmetric spaces with essentially different fundamental functions at zero can be defined by means of differential bases. Even the Lorentz and Marcinkiewicz or the Lebesgue and Marcinkiewicz spaces can be defined by means of differential bases.

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лИтЕРАтУРА

  1. M. гУсМАН,ДИФФЕРЕНц ИРОВАНИЕ ИНтЕгРАлОВ В Rn, МИР (МОскВА, 1978).

    Google Scholar 

  2. B. Jessen, J. Marcinkiewicz andA. Zygmund, Note on the differentiability of multiple integrals,Fund. Math.,25(1935), 217–234.

    Google Scholar 

  3. с. г. кРЕИН, У. И. пЕтУН ИИ ИE. M. сЕМЕНОВ,ИНтЕ РпОльцИь лИНЕИНых Оп ЕРАтОРОВ, НАУкА (МОск ВА, 1977).

    Google Scholar 

  4. A. Lebesgue, Sur l'intégration des fonctions discontinues,Ann. Sci. école Norm. Sup.,27(1910), 361–450.

    Google Scholar 

  5. J. Lindenstrauss andL. Tzafriri,Classical Banach spaces. I, II, Springer (Berlin, 1979).

    Google Scholar 

  6. B. Melero, A negative result in differentiation theory,Studia Math.,72(1982), 173–182.

    Google Scholar 

  7. S. Saks, On the strong derivatives of functions of integrals,Fund. Math.,25(1935), 235–252.

    Google Scholar 

  8. A. M. Stokolos, On the differentiation of integrals of functions fromLΦ(L),Studia Math.,88(1988), 103–120.

    Google Scholar 

  9. A. M. Stokolos, On the differentiation of integrals of functions from Orlicz classes,Studia Math.,94(1989), 35–50.

    Google Scholar 

  10. A. Zygmund, A note on the differentiability of multiple integrals,Colloq. Math.,16(1967), 199–204.

    Google Scholar 

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БЕРЕжНОИ, Е.И. О ДИФФЕРЕНцИРОВАНИИ ИНтЕгРАлОВ От ФУНкцИ И Иж сИММЕтРИЧНых пРОс тРАНстВ ДИФФЕРЕНцИАльНыМИ Б АжИсАМИ. Analysis Mathematica 22, 267–288 (1996). https://doi.org/10.1007/BF01904787

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  • DOI: https://doi.org/10.1007/BF01904787

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