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Displaying similar documents to “Hölder quasicontinuity in variable exponent Sobolev spaces.”

Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

Yan Lu, Yue Ping Zhu (2014)

Czechoslovak Mathematical Journal

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We introduce a new type of variable exponent function spaces M K ˙ q , p ( · ) α ( · ) , λ ( ℝ n ) of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents α and p are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators...

Variable Lebesgue norm estimates for BMO functions

Mitsuo Izuki, Yoshihiro Sawano (2012)

Czechoslovak Mathematical Journal

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In this paper, we are going to characterize the space BMO ( ℝ n ) through variable Lebesgue spaces and Morrey spaces. There have been many attempts to characterize the space BMO ( ℝ n ) by using various function spaces. For example, Ho obtained a characterization of BMO ( ℝ n ) with respect to rearrangement invariant spaces. However, variable Lebesgue spaces and Morrey spaces do not appear in the characterization. One of the reasons is that these spaces are not rearrangement invariant. We also obtain an analogue...