Douadi Drihem
Abstract
We introduce Herz-Sobolev spaces, which unify and generalize the classical Sobolev spaces. We will give a proof of the Sobolev-type embedding for these function spaces. All these results generalize the classical results on Sobolev spaces. Some remarks on Caffarelli--Kohn--Nirenberg inequality are given.
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We introduce Herz-Sobolev spaces, which unify and generalize the classical Sobolev spaces. We will give a proof of the Sobolev-type embedding for these function spaces. All these results generalize the classical results on Sobolev spaces. Some remarks on Caffarelli--Kohn--Nirenberg inequality are given.
Key concepts: Sobolev space, Sobolev inequality, Interpolation space, Mathematics, Embedding, Birnbaum–Orlicz space, Pure mathematics, Sobolev spaces for planar domains