Displaying similar documents to “Asymptotic growth of Cauchy transforms.”

Lower semicontinuity of multiple μ -quasiconvex integrals

Ilaria Fragalà (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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Lower semicontinuity results are obtained for multiple integrals of the kind ∫ ℝ n f ( x , ∇ μ u ) d μ , where μ is a given positive measure on ℝ n , and the vector-valued function u belongs to the Sobolev space H μ 1 , p ( ℝ n , ℝ m ) associated with μ . The proofs are essentially based on blow-up techniques, and a significant role is played therein by the concepts of tangent space and of tangent measures to μ . More precisely, for fully general μ , a notion of quasiconvexity for f along the tangent bundle to μ , turns out to be necessary...

Singular integrals and rectifiability.

Pertti Mattila (2002)

Publicacions Matemàtiques

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We shall discuss singular integrals on lower dimensional subsets of Rn. A survey of this topic was given in [M4]. The first part of this paper gives a quick review of some results discussed in [M4] and a survey of some newer results and open problems. In the second part we prove some results on the Riesz kernels in Rn. As far as I know, they have not been explicitly stated and proved, but they are very closely related to some earlier results and...

Poisson-like kernels in tube domains over light-cones

Gustavo Garrigós (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A family of holomorphic function spaces can be defined with reproducing kernels B α ⁢ z , w , obtained as real powers of the Cauchy-Szegö kernel. In this paper we study properties of the associated Poisson-like kernels: P α ⁢ z , w = B α ⁢ z , w 2 / B α ⁢ z , z . In particular, we show boundedness of associated maximal operators, and obtain formulas for the limit of Poisson integrals in the topological boundary of the cone.

Carleson measure and monogenic functions

S. Bernstein, P. Cerejeiras (2007)

Studia Mathematica

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We present necessary and sufficient conditions for a measure to be a p-Carleson measure, based on the Poisson and Poisson-Szegő kernels of the n-dimensional unit ball.