Geodesic
Gagliardo–Nirenberg inequality for maximal functions measuring smoothness
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 143-161 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove a Gagliardo–Nirenberg type pointwise interpolation inequality for special maximal functions, measuring smoothness in multidimensional case. It turns out that the clissical inequality follows from this one and it is also possible to use naturally a BMO terms in the inequality. 
@article{ZNSL_2011_389_a8,
     author = {E. Lokharu},
     title = {Gagliardo{\textendash}Nirenberg inequality for maximal functions measuring smoothness},
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     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a8/}
}
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E. Lokharu. Gagliardo–Nirenberg inequality for maximal functions measuring smoothness. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 143-161. http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a8/

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