Lebesgue points of two-dimensional Fourier transforms and strong summability

DOI10.1007/s00041-015-9393-2zbMath1333.42008OpenAlexW2061696633MaRDI QIDQ895431

Ferenc Weisz

Publication date: 3 December 2015

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-015-9393-2

zbMATH Keywords

Fourier transformsstrong summability\(\theta\)-summabilityMarcinkiewichz summabilitymodified Lebesgue points

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Summability in several variables (42B08) Summability and absolute summability of Fourier and trigonometric series (42A24)

Related Items

Multi-dimensional Fourier transforms, Lebesgue points and strong summability ⋮ Triangular Cesàro summability and Lebesgue points of two-dimensional Fourier series ⋮ Littlewood-Paley and finite atomic characterizations of anisotropic variable Hardy-Lorentz spaces and their applications ⋮ Almost everywhere strong \(C,1,0\) summability of 2-dimensional trigonometric Fourier series ⋮ On exponential summability of rectangular partial sums of double trigonometric Fourier series ⋮ Lebesgue points of double Fourier series and strong summability ⋮ \(\ell_1\)-summability and Lebesgue points of \(d\)-dimensional Fourier transforms ⋮ Triangular summability and Lebesgue points of 2-dimensional Fourier transforms ⋮ Lebesgue points of \(\ell_1\)-Cesàro summability of \(d\)-dimensional Fourier series ⋮ Cesàro summability and Lebesgue points of higher dimensional Fourier series ⋮ Summability of Fourier transforms on mixed-norm Lebesgue spaces via associated Herz spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Marcinkiewicz-summability of multi-dimensional Fourier transforms and Fourier series
• Marcinkiewicz-Fejér means of \(d\)-dimensional Walsh--Fourier series
• Points of strong summability of Fourier series
• The strong summability of Fourier transforms
• (\(C,\alpha\)) summability of Walsh--Kaczmarz--Fourier series
• A generalization for Fourier transforms of a theorem due to Marcinkiewicz
• Marcinkiewicz-\(\theta\)-summability of Fourier transforms
• Pointwise convergence of cone-like restricted two-dimensional \((C,1)\) means of trigonometric Fourier series
• Almost everywhere convergence of \((C,\alpha)\)-means of cubical partial sums of \(d\)-dimensional Walsh--Fourier series
• The Segal algebra \(\mathbf S_0(\mathbb R^d)\) and norm summability of Fourier series and Fourier transforms
• On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system
• Summability of Multi-Dimensional Fourier Series and Hardy Spaces
• Summability of Multi-Dimensional Trigonometric Fourier Series
• Wiener amalgams and pointwise summability of Fourier transforms and Fourier series
• A GENERALIZATION OF A THEOREM OF MARCINKIEWICZ
• Sur la Sommabilité Forte de Séries de Fourier
• On the summability of double Fourier series
• On the Convergence and Summability of Power Series on the Circle of Convergence (II)
• Points of strong summability of Fourier series