Hardy–Stein Type Identities and Rate of Growth of Mean Values of Functions in Generalized Hardy Spaces

Background: Upper extremity length and circumference abnormalities are present in a number of conditions in the pediatric population. In most cases, upper limb hypoplasia and hypertrophy are diagnosed when one limb appears substantially different from the other during physical examination. However, occasionally when this discrepancy exists, it can be difficult to determine which limb is the abnormal one. The purpose of this study was to establish normal values for upper extremity length, circumference, and rate of growth in children aged 0 to 17 years. Methods: In all, 377 participants had 4 measurements taken of each upper extremity: upper arm length, upper arm circumference, forearm length, and forearm circumference. Statistical analysis was performed to identify differences and rates of growth. Results: Mean values for arm and forearm length and circumference for each age, 0 to 17 years, were established. The determination of a child’s expected arm length is dependent on his or her height, age, and sex, while the calculation of a child’s expected forearm length depends on his or her weight, age, and sex. Male and female arms and forearms have similar growth rates of lengths and circumferences. No significant differences were found between right and left extremities for each of the 4 measurements taken. Conclusions: Contralateral limbs can be used for comparison of length and circumference of the arm and forearm in cases of unilateral upper extremity abnormality. The establishment of normal values for upper extremity length, circumference, and growth rate will be a useful diagnostic tool for upper extremity hypoplasia and hypertrophy.

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THE RATE OF INCREASE OF MEAN VALUES OF FUNCTIONS IN HARDY SPACES

Journal of the Australian Mathematical Society ◽

10.1017/s1446788708000414 ◽

2009 ◽

Vol 86 (2) ◽

pp. 199-204

Author(s):

JAVAD MASHREGHI

Keyword(s):

Hardy Space ◽

Hardy Spaces ◽

Mean Values ◽

Rate Of Increase

AbstractThe norm of a function f in the Hardy space Hp(𝔻) is by definition the limit of $\|f_r\|_p$ as r→1. We show that $d \|f_r\|_p/dr$ grows at most like o(1/log r) as r→1.

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Atomic decomposition and weak factorization in generalized Hardy spaces of closed forms

Bulletin des Sciences Mathématiques ◽

10.1016/j.bulsci.2017.07.004 ◽

2017 ◽

Vol 141 (7) ◽

pp. 676-702 ◽

Cited By ~ 1

Author(s):

Aline Bonami ◽

Justin Feuto ◽

Sandrine Grellier ◽

Luong Dang Ky

Keyword(s):

Hardy Spaces ◽

Atomic Decomposition ◽

Weak Factorization ◽

Generalized Hardy Spaces

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Determination of DNA Content of Aquatic Bacteria by Flow Cytometry

Applied and Environmental Microbiology ◽

10.1128/aem.67.4.1636-1645.2001 ◽

2001 ◽

Vol 67 (4) ◽

pp. 1636-1645 ◽

Cited By ~ 73

Author(s):

D. K. Button ◽

Betsy R. Robertson

Keyword(s):

Flow Cytometry ◽

Dna Content ◽

Mean Value ◽

Seawater Sample ◽

Cell Permeability ◽

Bacterial Isolates ◽

Mean Values ◽

Rate Of Growth ◽

Pure Cultures ◽

Specific Affinity

ABSTRACT The distribution of DNA among bacterioplankton and bacterial isolates was determined by flow cytometry of DAPI (4′,6′-diamidino-2-phenylindole)-stained organisms. Conditions were optimized to minimize error from nonspecific staining, AT bias, DNA packing, changes in ionic strength, and differences in cell permeability. The sensitivity was sufficient to characterize the small 1- to 2-Mb-genome organisms in freshwater and seawater, as well as low-DNA cells (“dims”). The dims could be formed from laboratory cultivars; their apparent DNA content was 0.1 Mb and similar to that of many particles in seawater. Preservation with formaldehyde stabilized samples until analysis. Further permeabilization with Triton X-100 facilitated the penetration of stain into stain-resistant lithotrophs. The amount of DNA per cell determined by flow cytometry agreed with mean values obtained from spectrophotometric analyses of cultures. Correction for the DNA AT bias of the stain was made for bacterial isolates with known G+C contents. The number of chromosome copies per cell was determined with pure cultures, which allowed growth rate analyses based on cell cycle theory. The chromosome ratio was empirically related to the rate of growth, and the rate of growth was related to nutrient concentration through specific affinity theory to obtain a probe for nutrient kinetics. The chromosome size of aMarinobacter arcticus isolate was determined to be 3.0 Mb by this method. In a typical seawater sample the distribution of bacterial DNA revealed two major populations based on DNA content that were not necessarily similar to populations determined by using other stains or protocols. A mean value of 2.5 fg of DNA cell−1was obtained for a typical seawater sample, and 90% of the population contained more than 1.1 fg of DNA cell−1.

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Some Generalized Hardy Spaces

Canadian Journal of Mathematics ◽

10.4153/cjm-1967-055-1 ◽

1967 ◽

Vol 19 ◽

pp. 621-628

Author(s):

L. D. Meeker

Keyword(s):

Banach Space ◽

Hardy Spaces ◽

Analytic Functions ◽

General Setting ◽

Classical Case ◽

Boundary Values ◽

Generalized Hardy Spaces

This paper is concerned with generalizations of the classical Hardy spaces (8, p. 39) and the question of boundary values for functions of these various spaces. The general setting is the “big disk” Δ discussed by Arens and Singer in (1, 2) and by Hoffman in (7). Analytic functions are defined in (1). Classes of such functions corresponding to the Hardy Hp spaces are considered and shown to possess boundary values in (2). Contrary to the classical case, such functions do not form a Banach space; hence they are not the functional analytic analogue of the classical spaces. In (3) quasi-analytic functions are defined while in (4) Hardy spaces of such functions are considered and are shown to have boundary values and to form a Banach space.

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