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Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces

J. García-Cuerva, K. Kazarian (1994)

Studia Mathematica

We study sufficient conditions on the weight w, in terms of membership in the A p classes, for the spline wavelet systems to be unconditional bases of the weighted space H p ( w ) . The main tool to obtain these results is a very simple theory of regular Calderón-Zygmund operators.

Ciesielski and Franklin systems

Gegham G. Gevorkyan (2006)

Banach Center Publications

A short survey of results on classical Franklin system, Ciesielski systems and general Franklin systems is given. The principal role of the investigations of Z. Ciesielski in the development of these three topics is presented. Recent results on general Franklin systems are discussed in more detail. Some open problems are posed.

Conjugacy for Fourier-Bessel expansions

Óscar Ciaurri, Krzysztof Stempak (2006)

Studia Mathematica

We define and investigate the conjugate operator for Fourier-Bessel expansions. Weighted norm and weak type (1,1) inequalities are proved for this operator by using a local version of the Calderón-Zygmund theory, with weights in most cases more general than A p weights. Also results on Poisson and conjugate Poisson integrals are furnished for the expansions considered. Finally, an alternative conjugate operator is discussed.

Conjugate martingale transforms

Ferenc Weisz (1992)

Studia Mathematica

Characterizations of H₁, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.

Consistency of trigonometric and polynomial regression estimators

Waldemar Popiński (1998)

Applicationes Mathematicae

The problem of nonparametric regression function estimation is considered using the complete orthonormal system of trigonometric functions or Legendre polynomials e k , k=0,1,..., for the observation model y i = f ( x i ) + η i , i=1,...,n, where the η i are independent random variables with zero mean value and finite variance, and the observation points x i [ a , b ] , i=1,...,n, form a random sample from a distribution with density ϱ L 1 [ a , b ] . Sufficient and necessary conditions are obtained for consistency in the sense of the errors f - f ^ N , | f ( x ) - N ( x ) | , x [ a , b ] ,...

Curriculum vita of Prof. Vasil Atanasov Popov

Ivanov, Kamen, Petrushev, Pencho (2002)

Serdica Mathematical Journal

Our primary goal in this preamble is to highlight the best of Vasil Popov’s mathematical achievements and ideas. V. Popov showed his extraordinary talent for mathematics in his early papers in the (typically Bulgarian) area of approximation in the Hausdorff metric. His results in this area are very well presented in the monograph of his advisor Bl. Sendov, “Hausdorff Approximation”.

Divergence of general operators on sets of measure zero

G. A. Karagulyan (2010)

Colloquium Mathematicae

We consider sequences of linear operators Uₙ with a localization property. It is proved that for any set E of measure zero there exists a set G for which U G ( x ) diverges at each point x ∈ E. This result is a generalization of analogous theorems known for the Fourier sum operators with respect to different orthogonal systems.

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