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Marcinkiewicz's theorem and its generalizations
2014In this thesis, we obtained some generaliszations of a theorem of Marcinkiewicz. The main tools of the proofs in this thesis are Weierstrass' approximation theorem, Lusin's theorem and Egoroff's theorem. In the one variable generalization, we will see that the statement holds even when we replace the closed and bounded interval I by R, the real line ...
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Journal of Soviet Mathematics, 1982
The relation is studied between the distribution of the zeros and the order of growth of entire analytic functions ϕ for which ¦ϕp(z)¦≤ ϕ(i Imz) for Imz ≥ 0, in particular, of entire characteristic functions of probability distributions. The main result is the following: if ρ1 is the exponent of convergence of the sequence of zeros of such a function ...
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The relation is studied between the distribution of the zeros and the order of growth of entire analytic functions ϕ for which ¦ϕp(z)¦≤ ϕ(i Imz) for Imz ≥ 0, in particular, of entire characteristic functions of probability distributions. The main result is the following: if ρ1 is the exponent of convergence of the sequence of zeros of such a function ...
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Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanato spaces
Approximation Theory and its Applications, 1995Let \(\Phi(r)\) be a positive increasing function on \((0,\infty)\), satisfying \(\Phi(2r)\leq D\Phi(r)\). For \(1\leq p\leq\infty\), the generalized Campanato space \({\mathcal E}^{p,\Phi}(\mathbb{R}^n)\) is the space of all locally integrable functions \(f\), such that for any cube \(Q\in\mathbb{R}^n\) with edge length \(r\), \(\int_Q|f(x)-f_Q|^p dx ...
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A GENERALIZATION OF A THEOREM OF MARCINKIEWICZ
Mathematics of the USSR-Izvestiya, 1968openaire +2 more sources
Two operators related to Marcinkiewicz integrals
Acta Mathematica Sinica, English Series, 2009Shan Zhen Lu
exaly
Generalized Marcinkiewicz Operators Aassociated to Twisted Surfaces
International Journal of Neutrosophic Scienceopenaire +1 more source
On regularity and weak regularity of functions generating Marcinkiewicz spaces
2000openaire +1 more source