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Weighted norm inequalities, offdiagonal estimates and elliptic operators, Part II: Offdiagonal estimates on spaces of homogeneous type
, 2005
"... Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the LaplaceBeltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincar ..."
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Cited by 22 (6 self)
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Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the LaplaceBeltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincaré inequalities. 1. Introduction and
COMMUTATORS OF SINGULAR INTEGRALS ON GENERALIZED L p SPACES WITH VARIABLE EXPONENT
, 2004
"... Abstract. A classical theorem of Coifman, Rochberg, and Weiss on commutators of singular integrals is extended to the case of generalized L p spaces with variable exponent. 1. ..."
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Cited by 3 (1 self)
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Abstract. A classical theorem of Coifman, Rochberg, and Weiss on commutators of singular integrals is extended to the case of generalized L p spaces with variable exponent. 1.
SHARP BOUNDS FOR GENERAL COMMUTATORS ON WEIGHTED LEBESGUE SPACES
"... Abstract. We show that if an operator T is bounded on weighted Lebesgue space L2 (w) and obeys a linear bound with respect to the A2 constant of the weight, then its commutator [b, T] with a function b in BMO will obey a quadratic bound with respect to the A2 constant of the weight. We also prove th ..."
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Cited by 1 (1 self)
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Abstract. We show that if an operator T is bounded on weighted Lebesgue space L2 (w) and obeys a linear bound with respect to the A2 constant of the weight, then its commutator [b, T] with a function b in BMO will obey a quadratic bound with respect to the A2 constant of the weight. We also prove that the kthorder commutator T k k−1 b = [b, Tb] will obey a bound that is a power (k + 1) of the A2 constant of the weight. Sharp extrapolation provides corresponding Lp (w) estimates. The results are sharp in terms of the growth of the operator norm with respect to the Ap constant of the weight for all 1 < p < ∞, all k, and all dimensions, as examples involving the Riesz transforms, power functions and power weights show. date: Feb82010 1.
WEIGHTED NORM INEQUALITIES FOR FRACTIONAL OPERATORS
, 2007
"... Abstract. We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relie ..."
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Cited by 1 (1 self)
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Abstract. We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a goodλ method that does not use any size or smoothness estimates for the kernels. 1.
Documenta Math. 607 Some Sharp Weighted Estimates for Multilinear Operators 1
, 2004
"... Abstract. In this paper, we establish a sharp inequality for some multilinear operators related to certain integral operators. The operators include CalderónZygmund singular integral operator, LittlewoodPaley operator, Marcinkiewicz operator and BochnerRiesz operator. As application, we obtain th ..."
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Abstract. In this paper, we establish a sharp inequality for some multilinear operators related to certain integral operators. The operators include CalderónZygmund singular integral operator, LittlewoodPaley operator, Marcinkiewicz operator and BochnerRiesz operator. As application, we obtain the weighted norm inequalities and Llog L type estimate for the multilinear operators.
ON A CALDERÓNZYGMUND COMMUTATORTYPE ESTIMATE
, 2007
"... In this paper we extend a CalderónZygmund commutatortype estimate. This estimate enables us to prove an embedding result concerning weighted function spaces. ..."
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In this paper we extend a CalderónZygmund commutatortype estimate. This estimate enables us to prove an embedding result concerning weighted function spaces.
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, 907
"... Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators ..."
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Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators
CONTINUITY FOR MAXIMAL COMMUTATOR OF BOCHNERRIESZ OPERATORS ON SOME WEIGHTED HARDY SPACES
, 2004
"... We show the boundedness for the commutator of BochnerRiesz operator on some weighted H 1 space. 1. ..."
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We show the boundedness for the commutator of BochnerRiesz operator on some weighted H 1 space. 1.
ACTA UNIVERSITATIS APULENSIS No 20/2009 BOUNDEDNESS FOR MULTILINEAR COMMUTATOR OF INTEGRAL OPERATOR ON HARDY AND HERZHARDY SPACES
"... b p) and (H ˙ K α,p q, b, ˙ Kα,p q) type boundedness for the multilinear commutator associated with some integral operator are obtained. 2000 Mathematics Subject Classification: 42B20, 42B25. 1. ..."
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b p) and (H ˙ K α,p q, b, ˙ Kα,p q) type boundedness for the multilinear commutator associated with some integral operator are obtained. 2000 Mathematics Subject Classification: 42B20, 42B25. 1.