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Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates

The Anh Bui, Jun Cao, Luong Dang Ky, Dachun Yang, Sibei Yang (2013)

Analysis and Geometry in Metric Spaces

Let X be a metric space with doubling measure and L a one-to-one operator of type ω having a bounded H∞ -functional calculus in L2(X) satisfying the reinforced (pL; qL) off-diagonal estimates on balls, where pL ∊ [1; 2) and qL ∊ (2;∞]. Let φ : X × [0;∞) → [0;∞) be a function such that φ (x;·) is an Orlicz function, φ(·;t) ∊ A∞(X) (the class of uniformly Muckenhoupt weights), its uniformly critical upper type index l(φ) ∊ (0;1] and φ(·; t) satisfies the uniformly reverse Hölder inequality of order...

Natural algebraic representation formulas for curves in ℂ³

Hubert Gollek (2002)

Banach Center Publications

We consider several explicit examples of solutions of the differential equation Φ₁’²(z) + Φ₂’²(z) + Φ₃’²(z) = d²(z) of meromorphic curves in ℂ³ with preset infinitesimal arclength function d(z) by nonlinear differential operators of the form (f,h,d) → V(f,h,d), V = (Φ₁,Φ₂,Φ₃), whose arguments are triples consisting of a meromorphic function f, a meromorphic vector field h, and a meromorphic differential 1-form d on an open set U ⊂ ℂ or, more general, on a Riemann surface Σ. Most of them are natural...

Navigating moduli space with complex twists

Curtis McMullen (2013)

Journal of the European Mathematical Society

We discuss a common framework for studying twists of Riemann surfaces coming from earthquakes, Teichmüller theory and Schiffer variations, and use it to analyze geodesics in the moduli space of isoperiodic 1-forms.

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