Startseite The Maximal Operator in Variable Spaces 饾惪 饾憹(路)(惟, 蟻) with Oscillating Weights
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The Maximal Operator in Variable Spaces 饾惪 饾憹(路)(惟, ) with Oscillating Weights

  • Vakhtang Kokilashvili , Natasha Samko und Stefan Samko
Ver枚ffentlicht/Copyright: 10. M盲rz 2010
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Georgian Mathematical Journal
Aus der Zeitschrift Band 13 Heft 1

Abstract

We study the boundedness of the maximal operator in the spaces 饾惪 饾憹(路)(惟, ) over a bounded open set 惟 in 饾憛饾憶 with the weight , where 饾懁饾憳 has the property that belongs to a certain Zygmund-type class. Weight functions 饾懁饾憳 may oscillate between two power functions with different exponents. It is assumed that the exponent 饾憹(饾懃) satisfies the Dini鈥揕ipschitz condition. The final statement on the boundedness is given in terms of index numbers of functions 饾懁饾憳 (similar in a certain sense to the Boyd indices for the Young functions defining Orlicz spaces).

Received: 2005-07-08
Published Online: 2010-03-10
Published in Print: 2006-March

漏 Heldermann Verlag

Heruntergeladen am 2.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/GMJ.2006.109/html
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