On the product theory of singular integrals
101 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/52203d34e7e067442617540fce2e7cb426038df6
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Vector-valued singular integrals and maximal functions on spaces of homogeneous type (2009, background): “This was pointed out in [13] but neither that proof nor the one in this paper has been previously published in this general framework with careful verification of all the details involved, some of which are rather delicate.”
- Localized Hardy Spaces $H^1$ Related to Admissible Functions on RD-Spaces and Applications to Schr\ (2009, unknown): “1”
- Multiparameter Hardy space theory on Carnot-Carathéodory spaces and product spaces of homogeneous type (2012, methodology): “Nagel and Stein proved the following Theorem 1.2 ([49]).”
- Littlewood–Paley characterizations for Hardy spaces on spaces of homogeneous type (2006, methodology): “Using this formula, we then establish an L theory for p ∈ (1,∞) for three kinds of Littlewood–Paley functions, which further completes the Littlewood–Paley theory on X developed in [32] when X is a boundary of an unbounded model domain of polynomial type in C(2); see Propositions 2.”
- A difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces (2009, background): “To this end, we first recall some basic estimates, which will be used throughout the whole paper, and whose proof can be found in [37, 16].”
- Boundedness of sublinear operators in Hardy spaces on RD-spaces via atoms (2008, background): “An important class of RD-spaces is provided by Carnot–Carathéodory spaces with a doubling measure; see, for example, [19,20].”
- FLAG HARDY SPACES AND MARCINKIEWICZ MULTIPLIERS ON THE HEISENBERG GROUP (2012, methodology): “…Lu 2010] have been adapted to some other multiparameter cases, such as the product spaces of Carnot–Carathéodory spaces [Han et al. 2013a], where the L p theory was established in [Nagel and Stein 2004], and the composition of two singular integrals with different homogeneity [Han et al. 2013b].”
- A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions☆ (2009, background): “2 apply in a wide range of settings, for instance, to Ahlfors n-regular metric measure spaces (see [22]), d-spaces (see [35]), Lie groups of the polynomial volume growth (see [36, 37, 29, 2]), the complete connected noncompact manifolds with a doubling measure (see [4, 5]), compact Carnot-Carathéodo”
- Hardy space theory on spaces of homogeneous type via orthonormal wavelet bases (2015, methodology): “ns ωi of the factor spaces Xi and on the H¨older regularity exponents ηi of the wavelets (Theorem 4.3). We remark that in this paper we concentrate on the product case. As Nagel and Stein observed in [NS1], “Any product theory tends to be burdened with notational complexities.” For notational simpli”