Multilinear Calderón–Zygmund Theory

By Loukas Grafakos, Rodolfo H. Torres. 2002

691 citations recorded by the source corpus.

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In Applied Mathematics

Citations in the corpus

MODULATION SPACES AND A CLASS OF BOUNDED MULTILINEAR PSEUDODIFFERENTIAL OPERATORS (2005, neutral): “B ´ ENYI, K. GR¨OCHENIG , C. HEIL, AND K. OKOUDJOU Marcinkiewicz multipliers, that use classical harmonic analysis techniques, see, e.g., [6], [12], [14].”
Extrapolation of Weighted norm inequalities for multivariable operators and applications (2004, methodology): “Multilinear CalderónZygmund operators were introduced and first studied by Coifman and Meyer [2], [3], [4], and later by Grafakos and Torres [11], [12].”
Hörmander type theorems for multi-linear and multi-parameter Fourier multiplier operators with limited smoothness (2014, methodology): “Results in [5–7] have been extended to multilinear Calderón–Zygmund operators by Kenig and Stein [8], Grafakos and Kalton [9], Grafakos and Torres [10], [11] to include 0 < r ≤ 1 (see also recent work of generalizations to bilinear square functions and vector-valued Calderón–Zygmund operators of Har”
Minimal smoothness conditions for bilinear Fourier multipliers (2013, background): “Grafakos–Torres [10] gave a general theory for multilinear Calderón– Zygmund operators and generalized the results of [3], [4], [15], and [14].”
Nonuniqueness of Weak Solutions to the SQG Equation (2016, methodology): “As opposed to [21, 52], which considers kernels of Calderón-Zygmund type, here we only need to consider kernelsKM that obey j ́j@ ́KM .”
Symbolic Calculus and the Transposes of Bilinear Pseudodifferential Operators (2003, positive): “Combining Theorem 1 with the result from [8] mentioned in Section 1, we recover the following.”
The Sharp Weighted Bound for Multilinear Maximal Functions and Calderón–Zygmund Operators (2012, methodology): “The theory of multilinear Calder´on-Zygmund operators originated in the works of Coifman and Meyer [3, 4] and was later developed by Christ and Journ´e [2], Kenig and Stein [10], and Grafakos and Torres [7].”
Extrapolation for multilinear compact operators and applications (2020, methodology): “39, 40 [18] L. Chaffee, R.H. Torres, and X. Wu, Multilinear weighted norm inequalities under integral type regular- ity conditions, Harmonic analysis, partial differential equations and applications, 193–216, Appl.”
New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory (2009, background): “It was shown in [25] that if 1 r1 + · · · + 1 rm = 1 r , then an m-linear Calderón–Zygmund operator satisfies T : L1 × · · · × Lm → L (2.”
The Hörmander multiplier theorem for multilinear operators (2012, methodology): “The multiplier theorem of Coifman and Meyer was extended to indices p 1 (and larger than 1/m by Grafakos and Torres [8] and Kenig and Stein [11] (when m = 2).”
Intuitive dyadic calculus: The basics (2015, background): “Historical notes Multilinear Calderón-Zygmund operators in the form considered in this book probably first appeared in Coifman and Meyer [1], but their systematic study was started by Grafakos and Torres [5].”