An elementary approach to several results on the Hardy-Littlewood maximal operator

By Andrei K. Lerner. 2008

91 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9349db30ebcfa7c71e87a62bd46775e4decce95b

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In Applied Mathematics

Citations in the corpus

Analysis in Banach Spaces (2023, methodology): “We have presented the simple approach to this theorem found by Lerner [2008]. The Extrapolation Theorem J.”
Sharp weighted estimates for classical operators (2010, background): “The exponent in Theorem 1.8 was first conjectured by Lerner [31] for the continuous square function; he also showed it was the best possible.”
Two weight norm inequalities for fractional integral operators and commutators (2014, background): “when α = 0 have played an important role in the proof of sharp constant inequalities: see [20, 57, 59].”
The Sharp Weighted Bound for Multilinear Maximal Functions and Calderón–Zygmund Operators (2012, methodology): “The sharp bound along the diagonal is obtained using similar methods to those found in [16] and these techniques only seem to work along the diagonal.”
Systems of dyadic cubes in a doubling metric space (2010, methodology): “A noteworthy feature of our argument is the circumvention of the use of the Besicovitch covering theorem, an essentially Euclidean device used in Lerner’s original proof, by the trivial covering properties exhibited by the adjacent dyadic systems.”
The Multilinear Strong Maximal Function (2010, background): “Some of the motivation for our work arises from the recent article by Lerner et al [18] where the multisublinear maximal function (1.1) M(f1, . . . , fm)(x) = sup Q3x Q cube m∏ i=1 1 |Q| ∫ Q |fi(yi)| dyi associated with cubes with sides parallel to the coordinate axes was introduced.”
Sharp Bekolle estimates for the Bergman projection (2012, background): “7) due to Lerner [19] that can be easily updated to this setting.”
New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory (2009, background): “Q ∣∣f (y)∣∣dy, satisfies M : L(w) → L(w) if and only if w is in Ap (see [38] for a new simple proof which yields the sharp Ap constant).”