Displaying similar documents to “May the Cauchy transform of a non-trivial finite measure vanish on the support of the measure?”

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...

Dichotomies for 𝐂 0 ( X ) and 𝐂 b ( X ) spaces

Szymon Głąb, Filip Strobin (2013)

Czechoslovak Mathematical Journal

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Jachymski showed that the set ( x , y ) ∈ 𝐜 0 × 𝐜 0 : ∑ i = 1 n α ( i ) x ( i ) y ( i ) n = 1 ∞ is bounded is either a meager subset of 𝐜 0 × 𝐜 0 or is equal to 𝐜 0 × 𝐜 0 . In the paper we generalize this result by considering more general spaces than 𝐜 0 , namely 𝐂 0 ( X ) , the space of all continuous functions which vanish at infinity, and 𝐂 b ( X ) , the space of all continuous bounded functions. Moreover, we replace the meagerness by σ -porosity.