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A Note on the Boundedness of the Hilbert Transform in Weighted Grand Lebesgue Spaces
-
Vakhtang Kokilashvili
und Alexander Meskhi
Veröffentlicht/Copyright:
10. MĂ€rz 2010
Abstract
It is proved that the Hilbert transform defined on a finite interval is bounded in the grand Lebesgue space
if and only if đ€ satisfies the Muckenhoupt condition đŽđ.
Key words and phrases:: Hilbert transform; weighted grand Lebesgue spaces; Muckenhoupt weight; one-weight inequality
Received: 2009-07-27
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 CesĂ ro Means of Conjugate Trigonometric Fourier Series
- Another Version of FugledeâPutnam 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 đżđ(·)([0, 1]) Spaces
- Rate of Approximation for Certain SzaszâMirakyanâDurrmeyer Operators
- On the (đ¶, α)-Means of Quadratic Partial Sums of Double WalshâKaczmarzâFourier Series
- Convergence in Measure of Partial Sums of Double VilenkinâFourier 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 HenstockâKurzweil Type Integral on a Compact-Zero Dimensional Metric Space
- T-Direction and Borel Direction of Algebroid Functions of Finite and Positive Order
Schlagwörter fĂŒr diesen Artikel
Hilbert transform;
weighted grand Lebesgue spaces;
Muckenhoupt weight;
one-weight inequality
Artikel in diesem Heft
- Boundary Value Problems for Fractional Differential Equations
- On the Approximate Properties of Generalized CesĂ ro Means of Conjugate Trigonometric Fourier Series
- Another Version of FugledeâPutnam 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 đżđ(·)([0, 1]) Spaces
- Rate of Approximation for Certain SzaszâMirakyanâDurrmeyer Operators
- On the (đ¶, α)-Means of Quadratic Partial Sums of Double WalshâKaczmarzâFourier Series
- Convergence in Measure of Partial Sums of Double VilenkinâFourier 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 HenstockâKurzweil Type Integral on a Compact-Zero Dimensional Metric Space
- T-Direction and Borel Direction of Algebroid Functions of Finite and Positive Order