| Title:
|
A two-weight inequality for the Bessel potential operator (English) |
| Author:
|
Rakotondratsimba, Y. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
497-511 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Necessary conditions and sufficient conditions are derived in order that \linebreak Bessel potential operator $J_{s,\lambda }$ is bounded from the weighted Lebesgue spaces $L_{v}^{p}=L^{p}(\Bbb R^n,v(x)dx)$ into $L_{u}^{q}$ when $1<p\leq q<\infty $. (English) |
| Keyword:
|
weighted inequalities |
| Keyword:
|
Bessel potential operators |
| Keyword:
|
Riesz potential operators |
| MSC:
|
26D10 |
| MSC:
|
42B20 |
| MSC:
|
42B25 |
| MSC:
|
46E35 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 0941.42007 |
| idMR:
|
MR1485071 |
| . |
| Date available:
|
2009-01-08T18:35:43Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118948 |
| . |
| Reference:
|
[Ad1] Adams D.R.: On the existence of capacity strong type estimates in $\Bbb R^n$.Ark. Mat. 14 (1976), 125-140. MR 0417774 |
| Reference:
|
[Ad2] Adams D.R.: Weighted nonlinear potential theory.Trans. Amer. Math. Soc. 297 (1986), 73-94. Zbl 0656.31012, MR 0849468 |
| Reference:
|
[Ad-Pi] Adams D.R.: Capacitary strong type estimates in semilinear problems.Ann. Inst. Fourier (Grenoble) 41 (1991), 117-135. Zbl 0741.35012, MR 1112194 |
| Reference:
|
[Ar-Sm] Aronszajn N., Smith K.: Theory of Bessel potentials.Ann. Inst. Fourier 11 Part I (1961), 385-475. Zbl 0102.32401, MR 0143935 |
| Reference:
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[Ch-Wh] Chanillo S., Wheeden R.: $L^p$ estimates for fractional integrals and Sobolev inequalities with applications to Schrödinger operators.Comm. Partial Differential Equations 10 (1985), 1077-1116. MR 0806256 |
| Reference:
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[Ke-Sa] Kerman R., Sawyer E.: Weighted norm inequalities for potentials with applications to Schrödinger operators, Fourier transform and Carleson measures.Ann. Inst. Fourier (Grenoble) 36 (1986), 207-228. MR 0766965 |
| Reference:
|
[Ma] Maz'ya V.G.: Sobolev Spaces.Springer-Verlag, Berlin-New York, 1985. Zbl 1152.46002, MR 0817985 |
| Reference:
|
[Ma-Ve] Maz'ya V.G., Verbitsky I.E.: Capacitary inequalities for fractional integrals, with applications to differential equations and SObolev multipliers.Ark. Mat. 33 (1995), 81-115. MR 1340271 |
| Reference:
|
[Sa-Wh] Sawyer E., Wheeden R.: Weighted inequalities for fractional integrals on euclidean and homogeneous spaces.Amer. J. Math. 114 (1992), 813-874. Zbl 0783.42011, MR 1175693 |
| Reference:
|
[Sc] Schechter M.: Multiplication operators.Canad. J. Math. LXI (1989), 234-249. Zbl 0665.46028, MR 1001610 |
| . |
