Extension theory for Sobolev spaces on open sets with Lipschitz boundaries

Burenkov, Viktor I.

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Guliyev, Emin V., Mammadov, Yagub Y. (2010)

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Maria Alessandra Ragusa (1999)

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In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class $H_{0}^{1, p} (Ω)$ for all $1 < p < \infty$ and, as a consequence, the Hölder regularity of the solution $u$ . $ℒ$ is an elliptic second order operator with discontinuous coefficients $(V M O)$ and the lower order terms belong to suitable Lebesgue spaces.

Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent

Ka Luen Cheung, Kwok-Pun Ho (2014)

Czechoslovak Mathematical Journal

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The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block...