Generalized Haar coefficients with power-law bounds characterize pixelated Lipschitz functions defined via dyadic pseudo-metrics on non-atomic probability spaces.
Guido Weiss: a few memories of a friend and an influential mathematician
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
This contribution starts with an exchange between us on the way we met Guido and he influenced our mathematical lives. Then it is mainly a survey paper that illustrates this influence by describing different topics and their subsequent evolution after his seminal papers and courses. Our main thread is the notion of a space of homogeneous type. In the second section we describe how it became central in pluricomplex analysis and consider particularly the existence of weak factorization for spaces of holomorphic functions. In the last section, one revisits the construction of a basis of wavelets in a space of homogeneous type and the way it allows a Littlewood-Paley analysis.
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A measure theoretic approach to Lipschitz regularity and its Haar type wavelet analysis
Generalized Haar coefficients with power-law bounds characterize pixelated Lipschitz functions defined via dyadic pseudo-metrics on non-atomic probability spaces.