Results 21 to 30 of about 4,227 (107)
Subdyadic square functions and applications to weighted harmonic analysis [PDF]
, 2015 Through the study of novel variants of the classical Littlewood–Paley–Stein g -functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on R d satisfying regularity hypotheses adapted to fine (subdyadic) scales ...
David Beltran, Jonathan Bennett
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Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrodinger operators [PDF]
Indiana University Mathematics Journal, 2017 In this paper we establish the product Hardy spaces associated with the Bessel Schr\"odinger operator introduced by Muckenhoupt and Stein, and provide equivalent characterizations in terms of the Bessel Riesz transforms, non-tangential and radial maximal
J. Betancor +4 more
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Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators [PDF]
, 2006 This is the third part of a series of four articles on weighted norm in- equalities, o-diagonal estimates and elliptic operators. For L in some class of elliptic operators, we study weighted norm L p inequalities for singular "non-integral" opera- tors ...
P. Auscher, J. M. Martell
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Real-variable characterizations of Musielak–Orlicz Hardy spaces on spaces of homogeneous type
, 2020 Let (X , d, μ) be a space of homogeneous type in the sense of Coifman and Weiss. In this article, the authors establish a complete real-variable theory of Musielak–Orlicz Hardy spaces on (X , d, μ).
Xing Fu, T. Ma, Dachun Yang
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Remarks on square functions in the Littlewood-Paley theory [PDF]
Bulletin of the Australian Mathematical Society, 1998 We prove that certain square function operators in the Littlewood-Paley theory defined by the kernels without any regularity are bounded on , 1 < p < ∞, w ∈ Ap (the weights of Muckenhoupt).
Shuichi Sato
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A priori bounds for the generalised parabolic Anderson model
Communications on Pure and Applied Mathematics, Volume 79, Issue 5, Page 1315-1394, May 2026.Abstract We show a priori bounds for solutions to (∂t−Δ)u=σ(u)ξ$(\partial _t - \Delta) u = \sigma (u) \xi$ in finite volume in the framework of Hairer's Regularity Structures [Invent Math 198:269–504, 2014]. We assume σ∈Cb2(R)$\sigma \in C_b^2 (\mathbb {R})$ and that ξ$\xi$ is of negative Hölder regularity of order −1−κ$- 1 - \kappa$ where κ<κ¯$\kappa <
Ajay Chandra +2 more
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Littlewood, Paley and almost‐orthogonality: a theory well ahead of its time
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract The classic paper by Littlewood and Paley [J. Lond. Math. Soc. (1), 6 (1931), 230–233] marked the birth of Littlewood–Paley theory. We discuss this paper and its impact from a historical perspective, include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them ...
Anthony Carbery
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Function spaces for decoupling
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We introduce new function spaces LW,sq,p(Rn)$\mathcal {L}_{W,s}^{q,p}(\mathbb {R}^{n})$ that yield a natural reformulation of the ℓqLp$\ell ^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half‐wave propagators, but not under all Fourier integral operators unless p=q$p=q$, in ...
Andrew Hassell +3 more
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Generalized quasi‐geostrophic equation in critical Lorentz–Besov spaces, based on maximal regularity
Mathematische Nachrichten, Volume 299, Issue 3, Page 637-660, March 2026.Abstract We consider the quasi‐geostrophic equation with its principal part (−Δ)α${(-\mathrm{\Delta})^{\alpha}}$ for α>1/2$\alpha >1/2$ in Rn$\mathbb {R}^n$ with n≥2$n \ge 2$. We show that for every initial data θ0∈Ḃr,q1−2α+nr$\theta _0 \in \dot{B}^{1-2\alpha + \frac{n}{r}}_{r, q}$ with 1
Hideo Kozono +2 more
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Discrete analogues of second‐order Riesz transforms
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Discrete analogues of classical operators in harmonic analysis have been widely studied, revealing deep connections with areas such as ergodic theory and analytic number theory. This line of research is commonly known as Discrete Analogues in Harmonic Analysis (DAHA).
Rodrigo Bañuelos, Daesung Kim
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