Local restriction theorem and maximal Bochner-Riesz operators for the Dunkl transforms

2018 ◽  
Vol 371 (1) ◽  
pp. 641-679 ◽  
Author(s):  
Feng Dai ◽  
Wenrui Ye
Keyword(s):  
Restriction Theorem ◽  
Riesz Operators ◽  
Local Restriction

Morrey spaces and boundedness of Bessel-Riesz operators

2021 ◽  
Author(s):  
Saba Mehmood ◽  
Eridani ◽  
Fatmawati
Keyword(s):  
Morrey Spaces ◽  
Riesz Operators

scholarly journals A note on Riesz operators

1976 ◽  
Vol 60 (1) ◽  
pp. 92-92 ◽  
Author(s):  
C. K. Chui ◽  
P. W. Smith ◽  
J. D. Ward
Keyword(s):  
Riesz Operators

SEMISTABILITY OF SYZYGY BUNDLES ON PROJECTIVE SPACES IN POSITIVE CHARACTERISTICS

2010 ◽  
Vol 21 (11) ◽  
pp. 1475-1504 ◽  
Author(s):  
V. TRIVEDI
Keyword(s):  
Line Bundle ◽  
Characteristic Zero ◽  
Projective Spaces ◽  
Restriction Theorem ◽  
Strong Restriction ◽  
Infinite Set

We generalize a result of Flenner, proved in characteristic zero, to positive characteristics. We prove that the first syzygy bundle, [Formula: see text], of the line bundle [Formula: see text] over [Formula: see text] is semistable, for a certain infinite set of integers d ≥ 0. Moreover, for arbitrary d, there is a "good enough estimate" on [Formula: see text] in terms of d and n; thus a strong restriction theorem of Langer, proved earlier for characteristic k > d, is valid in arbitrary characteristics.

Variable modes of formation for tonalite-trondhjemite-granodiorite-diorite (TTG)-related porphyry-type Cu ± Au deposits in the Neoarchean southern Abitibi subprovince (Canada): Evidence from petrochronology and oxybarometry

2021 ◽  
Author(s):  
Xuyang Meng ◽  
Jeremy P Richards ◽  
Daniel J Kontak ◽  
Adam C Simon ◽  
Jackie M Kleinsasser ◽  
...  
Keyword(s):  
Crustal Contamination ◽  
Edge Structure ◽  
Isotopic Signatures ◽  
Porphyry Cu ◽  
Abitibi Subprovince ◽  
Local Restriction ◽  
Fractionation Trend ◽  
Magma Crystallization ◽  
X Ray Absorption

Abstract Most known porphyry Cu ± Au deposits are associated with moderately oxidized and sulfur-rich, calc-alkaline to mildly alkalic arc-related magmas in the Phanerozoic. In contrast, sodium-enriched tonalite-trondhjemite-granodiorite-diorite (TTG) magmas predominant in the Archean are hypothesized to be unoxidized and sulfur-poor, which together preclude porphyry Cu deposit formation. Here, we test this hypothesis by interrogating the causative magmas for the ~2.7 Ga TTG-related Côté Gold, St-Jude, and Clifford porphyry-type Cu ± Au deposit settings in the Neoarchean southern Abitibi subprovince. New and previously published geochronological results constrain the age of emplacement of the causative magmas at ~2.74 Ga, ~2.70 Ga, and ~2.69 Ga, respectively. The dioritic and trondhjemitic magmas associated with Côté Gold and St-Jude evolved along a plagioclase-dominated fractionation trend, in contrast to amphibole-dominated fractionation for tonalitic magma at Clifford. Analyses of zircon grains from the Côté Gold, St-Jude, and Clifford igneous rocks yielded εHf(t) ± SD values of 4.5 ± 0.3, 4.2 ± 0.6, and 4.3 ± 0.4, and δ18O ± SD values of 5.40 ± 0.11 ‰, 3.91 ± 0.13 ‰, and 4.83 ± 0.12 ‰, respectively. These isotopic signatures indicate that although these magmas are mantle-sourced with minimal crustal contamination, for the St-Jude and Clifford settings the magmas or their sources may have undergone variable alteration by heated seawater or meteoric fluids. Primary barometric minerals (i.e., zircon, amphibole, apatite, and magnetite-ilmenite) that survived variable alteration and metamorphism (up to greenschist facies) were used for estimating fO2 of the causative magmas. Estimation of magmatic fO2 values, reported relative to the fayalite-magnetite-quartz buffer as ΔFMQ, using zircon geochemistry indicate that the fO2 values of the St-Jude, Côté Gold, and Clifford magmas increase from ΔFMQ -0.3 ± 0.6, ΔFMQ +0.8 ± 0.4, to ΔFMQ +1.2 ± 0.4, respectively. In contrast, amphibole chemistry yielded systematically higher fO2 values of ΔFMQ +1.6 ± 0.3 and ΔFMQ +2.6 ± 0.1 for Côté Gold and Clifford, respectively, which are consistent with previous studies that indicate amphibole may overestimate the fO2 of intrusive rocks by up to one log unit. Micro X-ray absorption near edge structure (μ-XANES) spectrometric determination of sulfur (i.e., S6+/ΣS) in primary apatite yielded ≥ΔFMQ -0.3 and ΔFMQ +1.4–1.8 for the St-Jude and Clifford, respectively. The magnetite-ilmenite mineral pairs from the Clifford tonalite yielded ΔFMQ +3.3 ± 1.3 at equilibrium temperatures of 634 ± 21 °C, recording the redox state of the late stage of magma crystallization. Electron probe microanalyses revealed that apatite grains from Clifford are enriched in S (up to 0.1 wt. %) relative to those of Côté Gold and St-Jude (below the detection limit), which is attributed to either relatively oxidized or sulfur-rich features of the Clifford tonalite. We interpret these results to indicate the deposits at Côté Gold and Clifford formed from mildly (~ΔFMQ +0.8 ± 0.4) to moderately (~ΔFMQ +1.5) oxidized magmas where voluminous early sulfide saturation was probably limited, whereas the St-Jude deposit represents a rare case whereby the ingress of externally derived hydrothermal fluids facilitated metal fertility in a relatively reduced magma chamber (~ΔFMQ +0). Furthermore, we conclude that variable modes of formation for these deposits and, in addition, the apparent rarity of porphyry-type Cu-Au deposits in the Archean may be attributed to either local restriction of favorable metallogenic conditions, and/or preservation, or an exploration bias.

scholarly journals Optimal Tone-Mapping for HDR Images

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3078-3080
Keyword(s):  
Dynamic Range ◽  
Optimization Problems ◽  
High Dynamic Range ◽  
Mapping Technique ◽  
Tone Mapping ◽  
Local Restriction ◽  
High Dynamic ◽  
M Estimation ◽  
Performance Gains ◽  
Smooth Transitions

This research paper proposes a unique optimal tone-mapping technique for high dynamic range (HDR) images, performing local adjustments with overlapping windows covering complete image. A local linear adjustment is applied on each window to preserve the radiance values. This problem may be treated as global optimization problems to satisfy the local restriction for every overlapping window. These Local constraints may be considered as a guidance map to suppress high contrast without losing its details. M-estimation technique may be used for solving this optimization problem. This technique may be applied to HDR images with sudden radiance changes or comparatively smooth transitions. Further, this technique may be applied to differentiate and analyzes HDR images from LDR images. Simulation results are included to support the performance gains achieved by the proposed technique.

scholarly journals Norm estimates for Bessel-Riesz operators on generalized Morrey spaces

2018 ◽  
Vol 143 (4) ◽  
pp. 409-417
Author(s):  
Mochammad Idris ◽  
Hendra Gunawan ◽  
Eridani
Keyword(s):  
Morrey Spaces ◽  
Generalized Morrey Spaces ◽  
Norm Estimates ◽  
Riesz Operators

scholarly journals NONCOMMUTATIVE DE LEEUW THEOREMS

2015 ◽  
Vol 3 ◽  
Author(s):  
MARTIJN CASPERS ◽  
JAVIER PARCET ◽  
MATHILDE PERRIN ◽  
ÉRIC RICARD
Keyword(s):  
Fourier Multiplier ◽  
Von Neumann Algebra ◽  
Modular Function ◽  
Discrete Subgroups ◽  
Original Proof ◽  
Restriction Theorem ◽  
Von Neumann ◽  
Lattice Approximation ◽  
Continuous Symbol ◽  
Group Von Neumann Algebra

Let $\text{H}$ be a subgroup of some locally compact group $\text{G}$. Assume that $\text{H}$ is approximable by discrete subgroups and that $\text{G}$ admits neighborhood bases which are almost invariant under conjugation by finite subsets of $\text{H}$. Let $m:\text{G}\rightarrow \mathbb{C}$ be a bounded continuous symbol giving rise to an $L_{p}$-bounded Fourier multiplier (not necessarily completely bounded) on the group von Neumann algebra of $\text{G}$ for some $1\leqslant p\leqslant \infty$. Then, $m_{\mid _{\text{H}}}$ yields an $L_{p}$-bounded Fourier multiplier on the group von Neumann algebra of $\text{H}$ provided that the modular function ${\rm\Delta}_{\text{G}}$ is equal to 1 over $\text{H}$. This is a noncommutative form of de Leeuw’s restriction theorem for a large class of pairs $(\text{G},\text{H})$. Our assumptions on $\text{H}$ are quite natural, and they recover the classical result. The main difference with de Leeuw’s original proof is that we replace dilations of Gaussians by other approximations of the identity for which certain new estimates on almost-multiplicative maps are crucial. Compactification via lattice approximation and periodization theorems are also investigated.

The commutators of Bochner-Riesz operators for elliptic operators

2021 ◽  
Vol 73 (3) ◽  
Author(s):  
Peng Chen ◽  
Xiaoxiao Tian ◽  
Lesley A. Ward
Keyword(s):  
Elliptic Operators ◽  
Riesz Operators

scholarly journals On Riesz operators

1969 ◽  
Vol 16 (3) ◽  
pp. 227-232 ◽  
Author(s):  
J. C. Alexander
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Operators ◽  
Image Position ◽  
Schauder’S Theorem

In (4) Vala proves a generalization of Schauder's theorem (3) on the compactness of the adjoint of a compact linear operator. The particular case of Vala's result that we shall be concerned with is as follows. Let t1 and t2 be non-zero bounded linear operators on the Banach spaces Y and X respectively, and denote by 1T2 the operator on B(X, Y) defined by

Leukocyte adhesion in local versus hemorrhage-induced ischemia

1992 ◽  
Vol 263 (3) ◽  
pp. H810-H815 ◽  
Author(s):  
M. A. Perry ◽  
D. N. Granger
Keyword(s):  
Endothelial Cell ◽  
Leukocyte Adhesion ◽  
Ischemia Reperfusion ◽  
Leukocyte Rolling ◽  
Leukocyte Adherence ◽  
Rolling Velocity ◽  
Local Ischemia ◽  
Cell Adhesive ◽  
Local Restriction ◽  
Adhesive Interactions

The objective of this study was to compare the leukocyte-endothelial cell adhesive interactions elicited in postcapillary venules by either local ischemia-reperfusion or hemorrhage-reperfusion. Leukocyte rolling, adherence, and emigration were monitored in cat mesenteric venules exposed to an 85% reduction in blood flow (induced by either hemorrhage or local restriction of arterial inflow) for 1 h, followed by 1 h reperfusion. Leukocyte-endothelial cell interactions, venular diameter, and red blood cell velocity were measured during baseline, ischemia, and reperfusion periods. Both local and hemorrhage-induced ischemia reperfusion caused a reduction in leukocyte rolling velocity and increases in leukocyte adherence and emigration. Quantitatively, the adherence and emigration responses in both ischemia models were nearly identical. However, the two models differed in their response to immunoneutralization of the leukocyte adhesion glycoprotein CD11/CD18 with monoclonal antibody (MAb) IB4. The MAb had a more profound effect in attenuating leukocyte adherence and emigration in the local ischemia model. These results indicate that different factors may contribute to leukocyte-endothelial cell adhesive interactions observed in local vs. systemic models of ischemia-reperfusion.

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