scholarly journals Convergence of $p$-adic pluricanonical measures to Lebesgue measures on skeleta in Berkovich spaces

2020 ◽  
Vol 7 ◽  
pp. 287-336
Author(s):  
Mattias Jonsson ◽  
Johannes Nicaise
Keyword(s):  
Berkovich Spaces ◽  
Lebesgue Measures

On a Choquet-Stieltjes type integral on intervals

2019 ◽  
Vol 69 (4) ◽  
pp. 801-814 ◽  
Author(s):  
Sorin G. Gal
Keyword(s):  
Lebesgue Measure ◽  
Choquet Integral ◽  
Stieltjes Integral ◽  
Line Integral ◽  
Type Integral ◽  
Choquet Integrals ◽  
Lebesgue Measures ◽  
Stieltjes Type

Abstract In this paper we introduce a new concept of Choquet-Stieltjes integral of f with respect to g on intervals, as a limit of Choquet integrals with respect to a capacity μ. For g(t) = t, one reduces to the usual Choquet integral and unlike the old known concept of Choquet-Stieltjes integral, for μ the Lebesgue measure, one reduces to the usual Riemann-Stieltjes integral. In the case of distorted Lebesgue measures, several properties of this new integral are obtained. As an application, the concept of Choquet line integral of second kind is introduced and some of its properties are obtained.

scholarly journals Characterizations of the lebesgue measure and product measures related to holomorphic functions having non-negative imaginary or real part

2020 ◽  
Vol 31 (12) ◽  
pp. 2050102
Author(s):  
Mitja Nedic
Keyword(s):  
Lebesgue Measure ◽  
Fourier Coefficients ◽  
Holomorphic Functions ◽  
Special Role ◽  
Borel Measures ◽  
Study Product ◽  
Nevanlinna Functions ◽  
Product Measures ◽  
Lebesgue Measures ◽  
Dimensional Lebesgue Measure

In this paper, we study a class of Borel measures on [Formula: see text] that arises as the class of representing measures of Herglotz-Nevanlinna functions. In particular, we study product measures within this class where products with the Lebesgue measures play a special role. Hence, we give several characterizations of the [Formula: see text]-dimensional Lebesgue measure among all such measures and characterize all product measures that appear in this class of measures. Furthermore, analogous results for the class of positive Borel measures on the unit poly-torus with vanishing mixed Fourier coefficients are also presented, and the relation between the two classes of measures with regard to the obtained results is discussed.

scholarly journals BMO Functions and Carleson Measures with Values in Uniformly Convex Spaces

2010 ◽  
Vol 62 (4) ◽  
pp. 827-844 ◽  
Author(s):  
Caiheng Ouyang ◽  
Quanhua Xu
Keyword(s):  
Equivalent Norm ◽  
Trigonometric Polynomials ◽  
Carleson Measures ◽  
Uniformly Convex ◽  
Bmo Functions ◽  
Smooth Norm ◽  
Converse Inequality ◽  
Lebesgue Measures ◽  
The Relationship ◽  
Vector Valued

AbstractThis paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let dA and dm denote Lebesgue measures on the unit disc D and the unit circle 𝕋, respectively. For 1 < q < ∞ and a Banach space B, we prove that there exists a positive constant c such thatholds for all trigonometric polynomials f with coefficients in B if and only if B admits an equivalent norm which is q-uniformly convex, whereThe validity of the converse inequality is equivalent to the existence of an equivalent q-uniformly smooth norm.

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