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. [3] GUSTAVSSON , J ., PEETRE , J . Interpolation of Orlicz spaces . Studia Math . 60 ( 1977 ), 33 – 59 . [4] SHESTAKOV , V. A . Transformations of Banch lattics and the interpolation of linear operators . Bull. Polish Sci. Math . 29
, On products of Orlicz spaces . Math. Ann ., 140 : 174 – 186 , 1960 . [6] C . Bennett and
Abstract
Let Φ(t)= ∫_0^t a(s) ds and Ψ(t)= ∫_0^t b(s) ds, where a(s) is a positive continuous function such that ∫_0^1 \frac{a(s)}{s} ds < ∞and ∫_1^{\∞}\frac{a(s)}{s} ds= +\∞, and b(s) is an increasing function such that \lim_{s\to\∞}b(s)= +\∞. Letw be a weight function and suppose that w∈A1\∩ A∞'. Then the following statements for the Hardy-Littlewood maximal function Mf(x) are equivalent:(I) there exist positive constants C
1 and C
2 such that
. 2007 Sharp Marchaud and converse inequalities in Orlicz spaces Proc. Amer. Math. Soc. 135 1115 – 1121 10.1090/S0002-9939-06-08682-5 . [17] Dunkl , C. F. , Xu , Y. 2001 Orthogonal
The maximal Orlicz spaces such that the mixed logarithmic means of multiple Walsh-Fourier series for the functions from these spaces converge in measure and in norm are found.
