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Optimal embeddings of generalized homogeneous Sobolev spaces

Tom 123 / 2011

Irshaad Ahmed, Georgi Eremiev Karadzhov Colloquium Mathematicum 123 (2011), 1-20 MSC: Primary 46E35; Secondary 46E30 DOI: 10.4064/cm123-1-1

Streszczenie

We prove optimal embeddings of homogeneous Sobolev spaces built over function spaces in ${\mathbb R}^n$ with $K$-monotone and rearrangement invariant norm into other rearrangement invariant function spaces. The investigation is based on pointwise and integral estimates of the rearrangement or the oscillation of the rearrangement of $f$ in terms of the rearrangement of the derivatives of $f$.

Autorzy

  • Irshaad AhmedAbdus Salam School of Mathematical Sciences
    GC University Lahore
    54600 Lahore, Pakistan
    e-mail
  • Georgi Eremiev KaradzhovAbdus Salam School of Mathematical Sciences
    GC University Lahore
    and
    Institute of Mathematics and Informatics
    Bulgarian Academy of Sciences
    1113 Sofia, Bulgaria
    e-mail

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