A two-weight inequality for the Bessel potential operator
Commentationes Mathematicae Universitatis Carolinae (1997)
- Volume: 38, Issue: 3, page 497-511
- ISSN: 0010-2628
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topRakotondratsimba, Yves. "A two-weight inequality for the Bessel potential operator." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 497-511. <http://eudml.org/doc/248088>.
@article{Rakotondratsimba1997,
abstract = {Necessary conditions and sufficient conditions are derived in order that Bessel potential operator $J_\{s,\lambda \}$ is bounded from the weighted Lebesgue spaces $L_\{v\}^\{p\}=L^\{p\}(\mathbb \{R\}^n,v(x)dx)$ into $L_\{u\}^\{q\}$ when $1<p\le q<\infty $.},
author = {Rakotondratsimba, Yves},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weighted inequalities; Bessel potential operators; Riesz potential operators; weighted inequalities; Bessel potential; Riesz potential},
language = {eng},
number = {3},
pages = {497-511},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A two-weight inequality for the Bessel potential operator},
url = {http://eudml.org/doc/248088},
volume = {38},
year = {1997},
}
TY - JOUR
AU - Rakotondratsimba, Yves
TI - A two-weight inequality for the Bessel potential operator
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 3
SP - 497
EP - 511
AB - Necessary conditions and sufficient conditions are derived in order that Bessel potential operator $J_{s,\lambda }$ is bounded from the weighted Lebesgue spaces $L_{v}^{p}=L^{p}(\mathbb {R}^n,v(x)dx)$ into $L_{u}^{q}$ when $1<p\le q<\infty $.
LA - eng
KW - weighted inequalities; Bessel potential operators; Riesz potential operators; weighted inequalities; Bessel potential; Riesz potential
UR - http://eudml.org/doc/248088
ER -
References
top- Adams D.R., On the existence of capacity strong type estimates in , Ark. Mat. 14 (1976), 125-140. (1976) MR0417774
- Adams D.R., Weighted nonlinear potential theory, Trans. Amer. Math. Soc. 297 (1986), 73-94. (1986) Zbl0656.31012MR0849468
- Adams D.R., Capacitary strong type estimates in semilinear problems, Ann. Inst. Fourier (Grenoble) 41 (1991), 117-135. (1991) Zbl0741.35012MR1112194
- Aronszajn N., Smith K., Theory of Bessel potentials, Ann. Inst. Fourier 11 Part I (1961), 385-475. (1961) Zbl0102.32401MR0143935
- Chanillo S., Wheeden R., estimates for fractional integrals and Sobolev inequalities with applications to Schrödinger operators, Comm. Partial Differential Equations 10 (1985), 1077-1116. (1985) MR0806256
- 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. (1986) MR0766965
- Maz'ya V.G., Sobolev Spaces, Springer-Verlag, Berlin-New York, 1985. Zbl1152.46002MR0817985
- 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. (1995) MR1340271
- Sawyer E., Wheeden R., Weighted inequalities for fractional integrals on euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813-874. (1992) Zbl0783.42011MR1175693
- Schechter M., Multiplication operators, Canad. J. Math. LXI (1989), 234-249. (1989) Zbl0665.46028MR1001610
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