We prove a Galiardo–Nirenberg type pointwise interpolation inequality for special maximal functions which measure smoothness in the multidimensional case. It turns out that the classsical inequality follows from this one; it is also possible to use naturally BMO norms in the inequality. Bibliography: 6 titles.
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Translated fron Zapiski Nauchnykh Seminarov POMI, Vol. 389, 2011, pp. 143–161.
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Lokharu, E. Gagliardo–Nirenberg inequality for maximal functions measuring smoothness. J Math Sci 182, 663–673 (2012). https://doi.org/10.1007/s10958-012-0771-x
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DOI: https://doi.org/10.1007/s10958-012-0771-x