Geodesic
Optimal embeddings of generalized homogeneous Sobolev spaces
Irshaad Ahmed 1   ; Georgi Eremiev Karadzhov 2
1 Abdus Salam School of Mathematical Sciences GC University Lahore 54600 Lahore, Pakistan
2 Abdus Salam School of Mathematical Sciences GC University Lahore and Institute of Mathematics and Informatics Bulgarian Academy of Sciences 1113 Sofia, Bulgaria
Colloquium Mathematicum, Tome 123 (2011) no. 1, pp. 1-20 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $f$.
DOI : 10.4064/cm123-1-1
Keywords: prove optimal embeddings homogeneous sobolev spaces built function spaces mathbb k monotone rearrangement invariant norm other rearrangement invariant function spaces investigation based pointwise integral estimates rearrangement oscillation rearrangement terms rearrangement derivatives

Irshaad Ahmed  1   ; Georgi Eremiev Karadzhov  2

1 Abdus Salam School of Mathematical Sciences GC University Lahore 54600 Lahore, Pakistan
2 Abdus Salam School of Mathematical Sciences GC University Lahore and Institute of Mathematics and Informatics Bulgarian Academy of Sciences 1113 Sofia, Bulgaria 
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Irshaad Ahmed; Georgi Eremiev Karadzhov. Optimal  embeddings of generalized homogeneous Sobolev  spaces. Colloquium Mathematicum, Tome 123 (2011) no. 1, pp. 1-20. doi: 10.4064/cm123-1-1

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