Concerning the energy class $_p$ for 0 < p < 1

Per Åhag; Rafał Czyż; Pham Hoàng Hiêp

Displaying similar documents to “Concerning the energy class $_{p}$ for 0 < p < 1”

A priori estimates for weak solutions of complex Monge-Ampère equations

Slimane Benelkourchi, Vincent Guedj, Ahmed Zeriahi (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $X$ be a compact Kähler manifold and $ω$ be a smooth closed form of bidegree $(1, 1)$ which is nonnegative and big. We study the classes $ℰ_{χ} (X, ω)$ of $ω$ -plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight $χ$ has fast growth at infinity, the corresponding functions are close to be bounded. We show that if a positive Radon measure is suitably dominated by the Monge-Ampère capacity, then it belongs to the range of the Monge-Ampère operator on some class $ℰ_{χ} (X, ω)$ . This is done by...

Green functions, Segre numbers, and King’s formula

Mats Andersson, Elizabeth Wulcan (2014)

Annales de l’institut Fourier

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Let $𝒥$ be a coherent ideal sheaf on a complex manifold $X$ with zero set $Z$ , and let $G$ be a plurisubharmonic function such that $G = log | f | + 𝒪 (1)$ locally at $Z$ , where $f$ is a tuple of holomorphic functions that defines $𝒥$ . We give a meaning to the Monge-Ampère products ${(d d^{c} G)}^{k}$ for $k = 0, 1, 2, ...$ , and prove that the Lelong numbers of the currents $M_{k}^{𝒥} : = 1_{Z} {(d d^{c} G)}^{k}$ at $x$ coincide with the so-called Segre numbers of $J$ at $x$ , introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, we show that $M_{k}^{𝒥}$ satisfy a certain...

The gradient lemma

Urban Cegrell (2007)

Annales Polonici Mathematici

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We show that if a decreasing sequence of subharmonic functions converges to a function in $W_{l o c}^{1, 2}$ then the convergence is in $W_{l o c}^{1, 2}$ .

On operators from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ or to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$

Christian Samuel (2010)

Colloquium Mathematicae

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We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.