Weighted Calderón–Zygmund and Rellich inequalities in Lp
We find necessary and sufficient conditions for the validity of weighted Rellich and Calderón–Zygmund inequalities with respect to L p -norm, 1 ≤ p ≤ ∞ , for functions in the whole space and in the half-space with Dirichlet boundary conditions. General operators like L = Δ + c x | x | 2 · ∇ - b | x...
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| Veröffentlicht in: | Mathematische annalen 2015, Vol.361 (1-2), p.313-366 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We find necessary and sufficient conditions for the validity of weighted Rellich and Calderón–Zygmund inequalities with respect to
L
p
-norm,
1
≤
p
≤
∞
, for functions in the whole space and in the half-space with Dirichlet boundary conditions. General operators like
L
=
Δ
+
c
x
|
x
|
2
·
∇
-
b
|
x
|
2
are considered. We compute best constants in some situations. |
|---|---|
| ISSN: | 0025-5831 1432-1807 |
| DOI: | 10.1007/s00208-014-1075-x |