Norm Inequalities Relating the Hilbert Transform to the Hardy-Littlewood Maximal Function

1981 ◽  
pp. 219-231 ◽  
Author(s):  
Benjamin Muckenhoupt
Keyword(s):  
Hilbert Transform ◽  
Maximal Function ◽  
Norm Inequalities ◽  
Littlewood Maximal Function ◽  
The Hilbert Transform

scholarly journals The Hilbert transform and maximal function along nonconvex curves in the plane

1994 ◽  
pp. 93-121 ◽  
Author(s):  
James Vance ◽  
Stephen Wainger ◽  
James Wright
Keyword(s):  
Hilbert Transform ◽  
Maximal Function ◽  
The Hilbert Transform

Weighted Lorentz Norm Inequalities for the One-Sided Hardy-Littlewood Maximal Functions and for the Maximal Ergodic Operator

1994 ◽  
Vol 46 (5) ◽  
pp. 1057-1072 ◽  
Author(s):  
P. Ortega Salvador
Keyword(s):  
Maximal Function ◽  
Maximal Operator ◽  
Measure Space ◽  
Maximal Functions ◽  
Norm Inequalities ◽  
Littlewood Maximal Function ◽  
Measure Preserving Transformation ◽  
The One ◽  
Image Position ◽  
Lorentz Norm

AbstractIn this paper we characterize weighted Lorentz norm inequalities for the one sided Hardy-Littlewood maximal functionSimilar questions are discussed for the maximal operator associated to an invertible measure preserving transformation of a measure space.

scholarly journals Norm inequalities relating one-sided singular integrals and the one-sided maximal function

2000 ◽  
Vol 69 (3) ◽  
pp. 403-414 ◽  
Author(s):  
M. S. Riveros ◽  
A. de la Torre
Keyword(s):  
Singular Integral ◽  
Maximal Function ◽  
Singular Integrals ◽  
Norm Inequalities ◽  
Littlewood Maximal Function ◽  
The One

AbstractIn this paper we prove that if a weight w satisfies the condition, then the Lp(w) norm of a one-sided singular integral is bounded by the Lp(w) norm of the one-sided Hardy-Littlewood maximal function, for 1 < p < q < ∞.

Norm Inequalities for Ultraspherical and Hankel Conjugate Functions

1975 ◽  
Vol 27 (1) ◽  
pp. 162-171 ◽  
Author(s):  
Kenneth F. Andersen
Keyword(s):  
Hilbert Transform ◽  
Conjugate Functions ◽  
Lebesgue Spaces ◽  
Norm Inequalities ◽  
Hankel Transforms ◽  
Weighted Lebesgue Spaces ◽  
The Hilbert Transform ◽  
Ultraspherical Expansions

The notion of conjugate functions associated with ultraspherical expansions and their continuous analogues, the Hankel transforms, was introduced by Muckenhoupt and Stein [14], to which we refer the reader for general background and an excellent discussion of the motivation underlying these notions. The operation of passing from a given function to its conjugate is in many ways analogous to the passage from a function to its Hilbert transform, indeed, Muckenhoupt and Stein proved, among other things, that these operations acting on appropriate weighted Lebesgue spaces, Lp(𝝁), satisfy inequalities of M. Riesz type analogous to those satisfied by the Hilbert transform on the usual Lebesgue spaces, Lv( — ∞, ∞).

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