Displaying similar documents to “ L p weighted inequalities for the dyadic square function”

Sharp L p -weighted Sobolev inequalities

Carlos Pérez (1995)

Annales de l'institut Fourier

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We prove sharp weighted inequalities of the form ∫ R n | f ( x ) | p v ( x ) d x ≤ C ∫ R n | q ( D ) ( f ) ( x ) | p N ( v ) ( x ) d x where q ( D ) is a differential operator and N is a combination of maximal type operator related to q ( D ) and to p .

Geometric Fourier analysis

Antonio Cordoba (1982)

Annales de l'institut Fourier

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In this paper we continue the study of the Fourier transform on R n , n ≥ 2 , analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of log ( N ) , where N is the number of equal angles considered in R 2 . The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of R n , n ≥ 2 ,...

Pointwise multipliers and corona type decomposition in B M O A

J. M. Ortega, Joan Fàbrega (1996)

Annales de l'institut Fourier

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In this paper we obtain several characterizations of the pointwise multipliers of the space B M O A in the unit ball B of ℂ n . Moreover, if g 1 , ... , g m are holomorphic functions on B , we prove that M g ( f ) ( z ) = ∑ j = 1 m g j ( z ) f j ( z ) maps B M O A × ... × B M O A onto B M O A if and only if the functions g j are multipliers of the space B M O A and satisfy ∑ j = 1 m | g j ( z ) | ≥ δ > 0 .

Linear forms in the logarithms of three positive rational numbers

Curtis D. Bennett, Josef Blass, A. M. W. Glass, David B. Meronk, Ray P. Steiner (1997)

Journal de théorie des nombres de Bordeaux

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In this paper we prove a lower bound for the linear dependence of three positive rational numbers under certain weak linear independence conditions on the coefficients of the linear forms. Let Λ = b 2 log α 2 - b 1 log α 1 - b 3 log α 3 ≠ 0 with b 1 , b 2 , b 3 positive integers and α 1 , α 2 , α 3 positive multiplicatively independent rational numbers greater than 1 . Let α j 1 = α j 1 / α j 2 with α j 1 , α j 2 coprime positive integers ( j = 1 , 2 , 3 ) . Let α j ≥ max { α j 1 , e } and assume that gcd ( b 1 , b 2 , b 3 ) = 1 . Let b ' = b 2 log α 1 + b 1 log α 2 b 2 log α 3 + b 3 log α 2 and assume that B ≥ max { 10 , log b ' } . We prove that either { b 1 , b 2 , b 3 } is c 4 , B -linearly dependent over ℤ (with respect to a 1 , a 2 , a 3 )...

Mapping properties of integral averaging operators

H. Heinig, G. Sinnamon (1998)

Studia Mathematica

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Characterizations are obtained for those pairs of weight functions u and v for which the operators T f ( x ) = ʃ a ( x ) b ( x ) f ( t ) d t with a and b certain non-negative functions are bounded from L u p ( 0 , ∞ ) to L v q ( 0 , ∞ ) , 0 < p,q < ∞, p≥ 1. Sufficient conditions are given for T to be bounded on the cones of monotone functions. The results are applied to give a weighted inequality comparing differences and derivatives as well as a weight characterization for the Steklov operator.

Hardy-Sobolev Inequalities for Hessian Integrals

Nunzia Gavitone (2007)

Bollettino dell'Unione Matematica Italiana

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Using appropriate symmetrization arguments, we prove the Hardy-Sobolev type inequalities for Hessian Integrals which extend the classical results, well known for Sobolev functions. For such inequalities the value of the best constant is given. Finally we give an improvement of these inequalities by adding a second term that, involves another singular weight which is a suitable negative power of log ⁡ ( | x | ) .