Results 1  10
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10
Risk communication
 Proceedings of the national conference on risk communication, Conservation Foundation,Washington, DC
, 1987
"... We consider Schrodinger semigroups e. IH, H =A+V on Iw ” with VcIxl ’ as 1x1rco, O<c<[(l/2)(n2)] * with H>O. We determine the exact power law divergence of I~e‘Hi~p,p and of some IIe‘Hlly,p as maps from Lp to Lq. The results are expressed most naturally in terms of the power a fo ..."
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Cited by 34 (1 self)
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We consider Schrodinger semigroups e. IH, H =A+V on Iw ” with VcIxl ’ as 1x1rco, O<c<[(l/2)(n2)] * with H>O. We determine the exact power law divergence of I~e‘Hi~p,p and of some IIe‘Hlly,p as maps from Lp to Lq. The results are expressed most naturally in terms of the power a for which there exists a positive resonance 9 such that Hq = 0, q(x) 1.x‘.:Ta 1991 Academic Press, Inc. 1.
Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials
, 2006
"... We show various L p estimates for Schrödinger operators −∆+V on R n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen [Sh1]. Our main tools are improved FeffermanPhong inequalities and reverse Hölder estimates for weak solutions of − ∆ + ..."
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Cited by 7 (3 self)
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We show various L p estimates for Schrödinger operators −∆+V on R n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen [Sh1]. Our main tools are improved FeffermanPhong inequalities and reverse Hölder estimates for weak solutions of − ∆ + V and their gradients.
Hardy inequalities for fractional integrals on general domains
 J. Funct. Anal
"... We prove a sharp Hardy inequality for fractional integrals for functions that are supported on a general domain. The constant is the same as the one for the halfspace and hence our result settles a recent conjecture of Bogdan and Dyda [2]. 1. ..."
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Cited by 2 (0 self)
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We prove a sharp Hardy inequality for fractional integrals for functions that are supported on a general domain. The constant is the same as the one for the halfspace and hence our result settles a recent conjecture of Bogdan and Dyda [2]. 1.
L pTHEORY FOR ELLIPTIC OPERATORS ON R d WITH SINGULAR COEFFICIENTS
"... Abstract. We study the generation of an analytic semigroup in L p (R d) and the determination of the domain for a class of second order elliptic operators with unbounded coefficients in R d. We also establish the maximal regularity of type L q –L p for the corresponding inhomogeneous parabolic equat ..."
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Abstract. We study the generation of an analytic semigroup in L p (R d) and the determination of the domain for a class of second order elliptic operators with unbounded coefficients in R d. We also establish the maximal regularity of type L q –L p for the corresponding inhomogeneous parabolic equation. In contrast to the previous literature the coefficients of the second derivatives are not required to be strictly elliptic or bounded. Interior singularities of the lower order terms are also discussed. Regularity properties of elliptic operators 1.
The HardyRellich Inequality for . . .
 PROC. ROY. SOC. EDINBURGH SECT. A
, 1999
"... The HardyRellich inequality given here generalizes a Hardy inequality of Davies [2], from the case of the Dirichlet Laplacian of a region\Omega ` R N to that of the higher order polyharmonic operators with Dirichlet boundary conditions. The inequality yields some immediate spectral information f ..."
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The HardyRellich inequality given here generalizes a Hardy inequality of Davies [2], from the case of the Dirichlet Laplacian of a region\Omega ` R N to that of the higher order polyharmonic operators with Dirichlet boundary conditions. The inequality yields some immediate spectral information for the polyharmonic operators and also bounds on the trace of the associated semigroups and resolvents.
Maximal Inequalities and Riesz transform estimates on . . .
, 2007
"... We show various L p estimates for Schrödinger operators −∆+V on R n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen [Sh1]. Our main tools are improved FeffermanPhong inequalities and reverse Hölder estimates for weak solutions of − ∆ + ..."
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We show various L p estimates for Schrödinger operators −∆+V on R n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen [Sh1]. Our main tools are improved FeffermanPhong inequalities and reverse Hölder estimates for weak solutions of − ∆ + V and their gradients.
license by Gordon and Breach Science Publishers Printed in Malaysia Remarks on the Hardy Inequality
, 1996
"... J. of lnequal. & Appl., 1997, Vol. 1, pp. 125137 Reprints available directly from the publisher Photocopying permitted by license only ..."
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J. of lnequal. & Appl., 1997, Vol. 1, pp. 125137 Reprints available directly from the publisher Photocopying permitted by license only