On a maximal theorem of Hardy and Littlewood and theorems concerning Fourier constants

1958 ◽  
Vol 69 (1) ◽  
pp. 418-422 ◽  
Author(s):  
Chen Yung-Ming
Keyword(s):  
Maximal Theorem

Convolution Estimates and Generalized de Leeuw Theorems for Multipliers of Weak Type (1,1)

1995 ◽  
Vol 47 (2) ◽  
pp. 225-245
Author(s):  
Nakhlé Asmar ◽  
Earl Berkson ◽  
T. A. Gillespie
Keyword(s):  
Abelian Group ◽  
Weak Type ◽  
Full Range ◽  
Locally Compact Abelian Group ◽  
Strong Type ◽  
Locally Compact ◽  
Linearization Methods ◽  
Maximal Theorem ◽  
Abstract Setting ◽  
Central Result

AbstractIn the context of a locally compact abelian group, we establish maximal theorem counterparts for weak type (1,1) multipliers of the classical de Leeuw theorems for individual strong multipliers. Special methods are developed to handle the weak type (1,1) estimates involved since standard linearization methods such as Lorentz space duality do not apply to this case. In particular, our central result is a maximal theorem for convolutions with weak type (1,1) multipliers which opens avenues of approximation. These results complete a recent series of papers by the authors which extend the de Leeuw theorems to a full range of strong type and weak type maximal multiplier estimates in the abstract setting.

Weighted fully measurable grand Lebesgue spaces and the maximal theorem

2016 ◽  
Vol 65 (1) ◽  
pp. 221-233 ◽  
Author(s):  
Giuseppina Anatriello ◽  
Maria Rosaria Formica
Keyword(s):  
Lebesgue Spaces ◽  
Maximal Theorem ◽  
Grand Lebesgue Spaces

scholarly journals A maximal theorem with function-theoretic applications

1930 ◽  
Vol 54 (0) ◽  
pp. 81-116 ◽  
Author(s):  
G. H. Hardy ◽  
J. E. Littlewood
Keyword(s):  
Maximal Theorem

Wave Front Sets, Local Smoothing and Bourgain's Circular Maximal Theorem

1992 ◽  
Vol 136 (1) ◽  
pp. 207 ◽  
Author(s):  
Gerd Mockenhaupt ◽  
Andreas Seeger ◽  
Christopher D. Sogge
Keyword(s):  
Wave Front ◽  
Local Smoothing ◽  
Maximal Theorem ◽  
Wave Front Sets

scholarly journals A Geometric Proof of the Strong Maximal Theorem

1975 ◽  
Vol 102 (1) ◽  
pp. 95 ◽  
Author(s):  
A. Corboda ◽  
R. Fefferman
Keyword(s):  
Geometric Proof ◽  
Maximal Theorem
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