Weak Hardy spaces and paraproducts

2016 ◽  
Author(s):  
◽  
Danqing He
Keyword(s):  
Hardy Spaces ◽  
Full Range ◽  
Square Function ◽  
University Of Missouri ◽  
Function Characterization ◽  
The University ◽  
Decomposition Of Distributions ◽  
Type Decomposition

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] The purpose of this dissertation is to provide a new square function characterization of weak Hardy spaces in the full range of exponents possible and use this characterization in applications on endpoint estimates for multilinear paraproducts. Additionally, we prove several maximal characterizations of weak Hardy spaces and obtain several properties of these spaces. Our main result is a Littlewood-Paley square function characterization of the Hardy spaces. Our proof is based on a Calderon-Zygmund type decomposition of distributions in Hardy spaces and on interpolation. Our results allow us to obtain endpoint estimates for several operators in terms of square function characterizations of weak L^p norms. As an application of this technique, we prove endpoint boundedness for mutlilinear paraproducts.

Non-tangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators

2015 ◽  
Vol 67 (5) ◽  
pp. 1161-1200 ◽  
Author(s):  
Junqiang Zhang ◽  
Jun Cao ◽  
Renjin Jiang ◽  
Dachun Yang
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Degenerate Elliptic Operators ◽  
Degenerate Elliptic Operator ◽  
Muckenhoupt Class ◽  
Degenerate Elliptic ◽  
Function Characterization

AbstractLet w be either in the Muckenhoupt class of A2(ℝn) weights or in the class of QC(ℝn) weights, and let be the degenerate elliptic operator on the Euclidean space ℝn, n ≥ 2. In this article, the authors establish the non-tangential maximal function characterization of the Hardy space associated with , and when with , the authors prove that the associated Riesz transform is bounded from to the weighted classical Hardy space .

Three studies in the philosophy of jazz

2018 ◽  
Author(s):  
◽  
Troy S. Hall
Keyword(s):  
Performance Practice ◽  
Full Range ◽  
Jazz Improvisation ◽  
Instrumental Performance ◽  
University Of Missouri ◽  
Vocal Jazz ◽  
The Third ◽  
Making Sense ◽  
The University ◽  
Comprehensive Discussion

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation comprises three studies which in turn discuss jazz ontology, jazz improvisation, and the question of whether jazz has ended as an artform. The first study discusses Andrew Kania's work on jazz ontology and attempts to clarify and extend his position regarding the principled exclusion of vocal jazz and jazz Fusion from his jazz ontology. Further, it introduces a quasi-realist strategy for making sense of jazz-work ontological discourse. The second study is a unique, comprehensive discussion of the jazz drummer's history and role in jazz improvisational contexts, in which the full range of instrumental performance practice (timekeeping, comping, and soloing) is explored. The third study is a provocative investigation of the possibility that the artform of jazz has "ended." Here, the end-of-art theses of Hegel and Danto are recalled and examined for their relevance in determining whether jazz has become a closed concept. The conclusion reached is that it is plausible to affirm that jazz has ended, even if it has not died.

Investigating the role of arginine 21 in the structure and function of human [alpha]a-crystallin

2018 ◽  
Author(s):  
◽  
Ashutosh Shripad Phadte
Keyword(s):  
Functional Characterization ◽  
Lens Fiber Cell ◽  
University Of Missouri ◽  
Mutant Proteins ◽  
Plausible Mechanism ◽  
And Function ◽  
The University

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Cataractogenesis in the eye lens occurs as a result of protein aggregation. Of the multiple mutations in [alpha]A-crystallins associated with the development of congenital hereditary cataract, three identified mutations target R21 within the N- terminal domain of the protein. On structural and functional characterization of a recently identified mutant of [alpha]A-crystallin, [alpha]A-R21Q, we revealed the contribution of R21 in dictating the interaction of [alpha]A-crystallin with other proteins. [alpha]A-R21Q showed and enhanced chaperone-like function, and increased binding to lens fiber cell membranes. Transduction of mutant proteins in ARPE-19 cells prevented their apoptosis in the presence of oxidative stress, suggesting a role for R21 in modulating the anti-apoptotic function of [alpha]A-crystallin. In addition, the R21Q point mutation rescued the chaperone-like activity of [alpha]A-G98R crystallin as well as palliated [alpha]A-G98R mediated cytotoxicity otherwise observed in transduction experiments. Although another mutation, R157Q rescued the chaperone-like activity of [alpha]A-G98R, the double mutant exhibited a loss of its cytoprotective function. The results therefore implicate an important role of R21 in regulating the functional aspect of [alpha]A-crystallin. [alpha]A-crystallin derived peptides have been shown to prevent non-specific aggregation of unfolding proteins in vitro. We show that the [alpha]A-crystallin derived mini-chaperone (mini-[alpha]A) mediated stabilization of self-aggregating [alpha]A-G98R crystallin and bovine [subscript]-crystallin occurs via compensation of lost surface charge. The observation therefore suggests a plausible mechanism of action of [alpha]A-crystallin derived peptides of therapeutic interest.

LITTLEWOOD–PALEY CHARACTERIZATION OF WEIGHTED HARDY SPACES ASSOCIATED WITH OPERATORS

2016 ◽  
Vol 103 (2) ◽  
pp. 250-267 ◽  
Author(s):  
GUORONG HU
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Adjoint Operator ◽  
Weighted Hardy Space ◽  
Boundedness Condition ◽  
Weighted Hardy Spaces ◽  
Lusin Area Function ◽  
Extra Assumption ◽  
Type Decomposition

Let$(X,d,\unicode[STIX]{x1D707})$be a metric measure space endowed with a distance$d$and a nonnegative, Borel, doubling measure$\unicode[STIX]{x1D707}$. Let$L$be a nonnegative self-adjoint operator on$L^{2}(X)$. Assume that the (heat) kernel associated to the semigroup$e^{-tL}$satisfies a Gaussian upper bound. In this paper, we prove that for any$p\in (0,\infty )$and$w\in A_{\infty }$, the weighted Hardy space$H_{L,S,w}^{p}(X)$associated with$L$in terms of the Lusin (area) function and the weighted Hardy space$H_{L,G,w}^{p}(X)$associated with$L$in terms of the Littlewood–Paley function coincide and their norms are equivalent. This improves a recent result of Duonget al.[‘A Littlewood–Paley type decomposition and weighted Hardy spaces associated with operators’,J. Geom. Anal.26(2016), 1617–1646], who proved that$H_{L,S,w}^{p}(X)=H_{L,G,w}^{p}(X)$for$p\in (0,1]$and$w\in A_{\infty }$by imposing an extra assumption of a Moser-type boundedness condition on$L$. Our result is new even in the unweighted setting, that is, when$w\equiv 1$.

LITTLEWOOD–PALEY CHARACTERIZATIONS OF ANISOTROPIC WEAK MUSIELAK–ORLICZ HARDY SPACES

2018 ◽  
Vol 237 ◽  
pp. 39-78
Author(s):  
BO LI ◽  
RUIRUI SUN ◽  
MINFENG LIAO ◽  
BAODE LI
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Growth Function ◽  
Anisotropic Growth ◽  
Area Function ◽  
Function Characterization ◽  
Lusin Area Function ◽  
Classical Hardy Space

Let $A$ be an expansive dilation on $\mathbb{R}^{n}$ and $\unicode[STIX]{x1D711}:\mathbb{R}^{n}\times [0,\infty )\rightarrow [0,\infty )$ an anisotropic growth function. In this article, the authors introduce the anisotropic weak Musielak–Orlicz Hardy space $\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$ via the nontangential grand maximal function and then obtain its Littlewood–Paley characterizations in terms of the anisotropic Lusin-area function, $g$-function or $g_{\unicode[STIX]{x1D706}}^{\ast }$-function, respectively. All these characterizations for anisotropic weak Hardy spaces $\mathit{WH}_{A}^{p}(\mathbb{R}^{n})$ (namely, $\unicode[STIX]{x1D711}(x,t):=t^{p}$ for all $t\in [0,\infty )$ and $x\in \mathbb{R}^{n}$ with $p\in (0,1]$) are new. Moreover, the range of $\unicode[STIX]{x1D706}$ in the anisotropic $g_{\unicode[STIX]{x1D706}}^{\ast }$-function characterization of $\mathit{WH}_{A}^{\unicode[STIX]{x1D711}}(\mathbb{R}^{n})$ coincides with the best known range of the $g_{\unicode[STIX]{x1D706}}^{\ast }$-function characterization of classical Hardy space $H^{p}(\mathbb{R}^{n})$ or its weighted variants, where $p\in (0,1]$.

An exploration of mechanisms for Arabidopsis TCP transcription factor activity at an interface of development and immunity

2018 ◽  
Author(s):  
◽  
Benjamin J. Spears
Keyword(s):  
Receptor Gene ◽  
Direct Interaction ◽  
Sequence Motifs ◽  
Crop Species ◽  
University Of Missouri ◽  
Agriculture And Food ◽  
The University

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] "The work presented in this dissertation aimed to characterize new functions and regulatory targets for TCP8, potentially in both defense and development signaling networks. Using in vitro and in vivo promoter interaction screens in yeast and Arabidopsis, respectively, the PTI-related immune receptor gene EFR as well as a set of growth-related BR signaling genes were identified as regulatory targets of TCP8; these findings were verified through direct interaction assays characterization of tcp mutants for associated phenotypes. Additionally, SRFR1-interacting TCPs were shown to be post-translationally modified by SUMO proteins, alongside data suggesting that SRFR1 sequence motifs that facilitate interactions with SUMO are critical to its function. Together, these data describe novel roles for TCP8 and other class I TCPs, as well as novel regulatory mechanisms for their activities in the context of their interactions with SRFR1 and other TPR proteins. As a highly-conserved TF family among plants, including economically relevant crop species, advancing our understanding of TCP regulatory activities could eventually yield translational benefits to agriculture and food production worldwide."--Page 36-37.

Molecular dissection of meiotic silencing by unpaired DNA

2015 ◽  
Author(s):  
◽  
Logan M. Decker
Keyword(s):  
Messenger Rnas ◽  
Meiotic Silencing ◽  
University Of Missouri ◽  
A Genome ◽  
Unpaired Region ◽  
The University ◽  
Surveillance Mechanism ◽  
Interfering Rna ◽  
Identification And Characterization

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Meiotic silencing by unpaired DNA (MSUD) is a genome surveillance mechanism that uses RNAi to protect against genetic parasites such as retrotransposons and viruses. This is accomplished by scanning the genome for DNA segments not paired with a homologous partner during meiosis and targeting the corresponding messenger RNAs for destruction. MSUD begins when a single-stranded RNA is made from the unpaired region and subsequently converted into small interfering RNA (siRNA), which are used as sequence specific guides for mRNA destruction. To date, nine meiotic silencing genes have been characterized and here we report the identification and characterization of two new candidates that are orthologous to the conserved proteins CBP80 and EPS15.

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