On vector-valued Fourier multiplier theorems
Frank Zimmermann (1989)
Studia Mathematica
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Frank Zimmermann (1989)
Studia Mathematica
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Bruce Aubertin, John Fournier (1993)
Studia Mathematica
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We show that, if the coefficients (an) in a series tend to 0 as n → ∞ and satisfy the regularity condition that , then the cosine series represents an integrable function on the interval [-π,π]. We also show that, if the coefficients (bn) in a series tend to 0 and satisfy the corresponding regularity condition, then the sine series represents an integrable function on [-π,π] if and only if . These conclusions were previously known to hold under stronger restrictions on the sizes...
Ferenc Móricz (1992)
Studia Mathematica
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In 1970 C. W. Onneweer formulated a sufficient condition for a periodic W-continuous function to have a Walsh-Fourier series which converges uniformly to the function. In this paper we extend his results from single to double Walsh-Fourier series in a more general setting. We study the convergence of rectangular partial sums in -norm for some 1 ≤ p ≤ ∞ over the unit square [0,1) × [0,1). In case p = ∞, by we mean , the collection of uniformly W-continuous functions f(x, y), endowed...
Michał Wojciechowski (2000)
Studia Mathematica
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An integral criterion for being an Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.
Earl Berkson, T. Gillespie (1994)
Studia Mathematica
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We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X. ...
Bartolomé Barceló (1986)
Studia Mathematica
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V. Kolyada (1997)
Studia Mathematica
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We investigate the Fourier transforms of functions in the Sobolev spaces . It is proved that for any function the Fourier transform f̂ belongs to the Lorentz space , where . Furthermore, we derive from this result that for any mixed derivative the weighted norm can be estimated by the sum of -norms of all pure derivatives of the same order. This gives an answer to a question posed by A. Pełczyński and M. Wojciechowski.
Ferenc Weisz (1996)
Studia Mathematica
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It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space to (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type . As a consequence we show that the dyadic integral of a ∞ function is dyadically differentiable and its derivative is f a.e.
Wolodymyr Madych (1974)
Studia Mathematica
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George Gasper, Walter Trebels (1979)
Studia Mathematica
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Jürgen Marschall (1987)
Studia Mathematica
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Okuyama, Yasuo (1983-1984)
Portugaliae mathematica
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G. Gát (1998)
Studia Mathematica
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Let G be the Walsh group. For we prove the a. e. convergence σf → f(n → ∞), where is the nth (C,1) mean of f with respect to the Walsh-Kaczmarz system. Define the maximal operator We prove that σ* is of type (p,p) for all 1 < p ≤ ∞ and of weak type (1,1). Moreover, , where H is the Hardy space on the Walsh group.