Lorentz spaces with variable exponents

By H. Kempka, Jan Vyb'iral. 2012

81 citations recorded by the source corpus.

We introduce Lorentz spaces Lp(·),q(Rn) and Lp(·),q(·)(Rn) with variable exponents. We prove several basic properties of these spaces including embeddings and the identity Lp(·),p(·)(Rn)=Lp(·)(Rn) . We also show that these spaces arise through real interpolation between Lp(·)(Rn) and L∞(Rn) . Furthermore, we answer in a negative way the question posed in whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/2a1d316bbc0a4747fb7e231d6259542e5fc97c91

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In Applied Mathematics

1. Yong Jiao
2. Dejian Zhou
3. Lian Wu
4. Yahui Zuo

Citations in the corpus

• Variable Hardy–Lorentz spaces Hp(·),q(Rn) (2018, methodology): “While, the variable Lorentz space given by Kempka and Vybíral could, namely, we have 𝐿𝑝(⋅),𝑝(⋅)(ℝ𝑛) = 𝐿𝑝(⋅)(ℝ𝑛).”