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On the Integrability and Uniform Convergence of Multiplicative Fourier Transforms
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Boris I. Golubov
Veröffentlicht/Copyright:
10. März 2010
Abstract
Analogues of two Hardy–Littlewood theorems are proved for a multiplicative Fourier transform. A Szasz type condition for a multiplicative Fourier transform is given and its nonimprovability is proved. Besides, an analogue of Ul'yanov's theorem on the uniform convergence of a trigonometric series and an analogue of Konyuškov–Stechkin's embedding theorem are obtained by means of a Nikol'skii type inequality of various metrics.
Key words and phrases:: Multiplicative Fourier transform; integrability; uniform convergence; Nikol'skii type inequality
Received: 2009-07-16
Published Online: 2010-03-10
Published in Print: 2009-September
© Heldermann Verlag
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Artikel in diesem Heft
- Boundary Value Problems for Fractional Differential Equations
- On the Approximate Properties of Generalized Cesàro Means of Conjugate Trigonometric Fourier Series
- Another Version of Fuglede–Putnam Theorem
- On Divergence of Fourier Series with Respect to Multiplicative Systems on the Sets of Measure Zero
- Uniqueness of Entire or Meromorphic Functions Concerning Differential Polynomials
- An Almost Greedy Uniformly Bounded Orthonormal Basis in 𝐿𝑝(·)([0, 1]) Spaces
- Rate of Approximation for Certain Szasz–Mirakyan–Durrmeyer Operators
- On the (𝐶, α)-Means of Quadratic Partial Sums of Double Walsh–Kaczmarz–Fourier Series
- Convergence in Measure of Partial Sums of Double Vilenkin–Fourier Series
- On the Exponential Uniform Strong Summability of Multiple Trigonometric Fourier Series
- On the Integrability and Uniform Convergence of Multiplicative Fourier Transforms
- A Note on the Boundedness of the Hilbert Transform in Weighted Grand Lebesgue Spaces
- Necessary Conditions for Integrability of the Fourier Transform
- The Diagonal Mapping in Bmoa-Type Spaces of Analytic Functions on the Polydisk
- Representation of Quasi-Measure by Henstock–Kurzweil Type Integral on a Compact-Zero Dimensional Metric Space
- T-Direction and Borel Direction of Algebroid Functions of Finite and Positive Order
Schlagwörter für diesen Artikel
Multiplicative Fourier transform;
integrability;
uniform convergence;
Nikol'skii type inequality
Artikel in diesem Heft
- Boundary Value Problems for Fractional Differential Equations
- On the Approximate Properties of Generalized Cesàro Means of Conjugate Trigonometric Fourier Series
- Another Version of Fuglede–Putnam Theorem
- On Divergence of Fourier Series with Respect to Multiplicative Systems on the Sets of Measure Zero
- Uniqueness of Entire or Meromorphic Functions Concerning Differential Polynomials
- An Almost Greedy Uniformly Bounded Orthonormal Basis in 𝐿𝑝(·)([0, 1]) Spaces
- Rate of Approximation for Certain Szasz–Mirakyan–Durrmeyer Operators
- On the (𝐶, α)-Means of Quadratic Partial Sums of Double Walsh–Kaczmarz–Fourier Series
- Convergence in Measure of Partial Sums of Double Vilenkin–Fourier Series
- On the Exponential Uniform Strong Summability of Multiple Trigonometric Fourier Series
- On the Integrability and Uniform Convergence of Multiplicative Fourier Transforms
- A Note on the Boundedness of the Hilbert Transform in Weighted Grand Lebesgue Spaces
- Necessary Conditions for Integrability of the Fourier Transform
- The Diagonal Mapping in Bmoa-Type Spaces of Analytic Functions on the Polydisk
- Representation of Quasi-Measure by Henstock–Kurzweil Type Integral on a Compact-Zero Dimensional Metric Space
- T-Direction and Borel Direction of Algebroid Functions of Finite and Positive Order
