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Keywords:
weighted inequalities; Bessel potential operators; Riesz potential operators
weighted inequalities; Bessel potential operators; Riesz potential operators
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 $.
References:
[Ad1] Adams D.R.: On the existence of capacity strong type estimates in $\Bbb R^n$. Ark. Mat. 14 (1976), 125-140. MR 0417774
[Ad2] Adams D.R.: Weighted nonlinear potential theory. Trans. Amer. Math. Soc. 297 (1986), 73-94. MR 0849468 | Zbl 0656.31012
[Ad-Pi] Adams D.R.: Capacitary strong type estimates in semilinear problems. Ann. Inst. Fourier (Grenoble) 41 (1991), 117-135. MR 1112194 | Zbl 0741.35012
[Ar-Sm] Aronszajn N., Smith K.: Theory of Bessel potentials. Ann. Inst. Fourier 11 Part I (1961), 385-475. MR 0143935 | Zbl 0102.32401
[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
[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
[Ma] Maz'ya V.G.: Sobolev Spaces. Springer-Verlag, Berlin-New York, 1985. MR 0817985 | Zbl 1152.46002
[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
[Sa-Wh] Sawyer E., Wheeden R.: Weighted inequalities for fractional integrals on euclidean and homogeneous spaces. Amer. J. Math. 114 (1992), 813-874. MR 1175693 | Zbl 0783.42011
[Sc] Schechter M.: Multiplication operators. Canad. J. Math. LXI (1989), 234-249. MR 1001610 | Zbl 0665.46028
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