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- Cristina Pereyra
- 1999

In this paper we construct a family of divergence-free multiwavelets. The construction follows Lemari e's procedure. In the process we nd multiresolution analyses (MRA) related by diierentiation and integration to a family of biorthogonal MRAs constructed by Hardin and Marasovich. The multiscaling and multiwavelets constructed have symmetries and support… (More)

We show that if an operator T is bounded on weighted Lebesgue space L 2 (w) and obeys a linear bound with respect to the A 2 constant of the weight, then its commutator [b, T ] with a function b in BM O will obey a quadratic bound with respect to the A 2 constant of the weight. We also prove that the kth-order commutator T k b = [b, T k−1 b ] will obey a… (More)

- JEAN CARLO MORAES, CRISTINA PEREYRA, M. C. PEREYRA
- 2013

We extend the definitions of dyadic paraproduct and t-Haar multipliers to dyadic operators that depend on the complexity (m, n), for m and n natural numbers. We use the ideas developed by Nazarov and Volberg in [NV] to prove that the weighted L 2 (w)-norm of a paraproduct with complexity (m, n), associated to a function b ∈ BM O d , depends linearly on the… (More)

x0 Introduction In this paper, we prove suucient conditions on pairs of weights (u; v) (scalar, matrix or operator valued) so that the Hilbert transform Hf(x) = p: v: Z f(y) x ? y dy; is bounded from L 2 (u) to L 2 (v). When u = v are scalar, the classical results were given in HMW] and CF]. Earlier, HS] gave a characterization of these weights by complex… (More)

- Oleksandra V. Beznosova, Cristina Pereyra
- 2008

The dyadic paraproduct is bounded in weighted Lebesgue spaces Lp(w) if and only if the weight w belongs to the Muckenhoupt class A d p. However, the sharp bounds on the norm of the dyadic paraproduct are not known even in the simplest L2(w) case. In this paper we prove the linear bound on the norm of the dyadic paraproduct in the weighted Lebesgue space… (More)

- Nuriye Atasever, Cristina Pereyra, Pedro Embid, Anna Skripka, NURIYE ATASEVER, Thomas Hytönen
- 2014

- OLEKSANDRA BEZNOSOVA, JEAN CARLO MORAES, CRISTINA PEREYRA, Tuomas Hytönen, M. C. PEREYRA
- 2013

We show that if a weight w ∈ C d 2t and there is q > 1 such that w 2t ∈ A d q , then the L 2-norm of the t-Haar multiplier of complexity (m, n) associated to w depends on the square root of the C d 2t-characteristic of w times the square root A d q-characteristic of w 2t times a constant that depends polynomially on the complexity. In particular, if w ∈ C d… (More)

We survey the recent solution of the so-called A 2 conjecture, all Calderón-Zygmund singular integral operators are bounded on L 2 (w) with a bound that depends linearly on the A 2 characteristic of the weight w, as well as corresponding results for commutators. We highlight the interplay of dyadic harmonic analysis in the solution of the A 2 conjecture,… (More)

To my parents, Seung-Guk and Soon-Rye, for their support, encouragement and love. " And now these three remain: faith, hope and love. But the greatest of these is love " – Corinthians 13.13 iv Acknowledgments I am heartily thankful to my graduate advisor, Dr. María Cristina Pereyra, whose encouragement, guidance and support helped me in all the time of… (More)

Contents Introduction xv Chapter 1. Fourier series: some motivation 1 1.1. Some examples and key definitions 1 1.2. Main questions 5 1.3. Fourier series and Fourier coefficients 7 1.4. A little history, and motivation from the physical world 11 Chapter 2. Interlude 17 2.1. Nested classes of functions on bounded intervals 17 2.2. Modes of convergence 28 2.3.… (More)