Boundedness of Some Paraproducts on Spaces of Homogeneous Type

Let (X,d,μ) be a space of homogeneous type in the sense of Coifman and Weiss. In this article, the author develops a partial theory of paraproducts {Πj}j=13 defined via approximations of the identity with exponential decay (and integration 1), which are extensions of paraproducts defined via regular wavelets. Precisely, the author first obtains the boundedness of Π3 on Hardy spaces and then, via the methods of interpolation and the well-known T(1) theorem, establishes the endpoint estimates for {Πj}j=13. The main novelty of this paper is the application of the Abel summation formula to the establishment of some relations among the boundedness of {Πj}j=13, which has independent interests. It is also remarked that, throughout this article, μ is not assumed to satisfy the reverse doubling condition.

Longline Hook Selectivity for Branchiostegus japonicus (Houttuyn, 1782) and Dentex tumifrons (Temminck & Schlegel, 1843) in the East China Sea

Bottom longline fishing of red tilefish (Branchiostegus japonicus) is one of the most important commercial of fishing in the East China Sea. The present study aimed to investigate hook selectivity in B. japonicus and D. tumifrons, by means of experiments using three hook sizes (“J”: #15, #13 and #11) and was conducted in the East China Sea from June to August 2018. Altogether 602 B. japonicus fish and 858 D. tumifrons fish were caught. With respect to the size of the hook used, the total length-frequency varied significantly for both B. japonicus and D. tumifrons that were caught. The total length and four mouth parameters (upper and lower jaw length as well as height and width of mouth opening) of the two species showed a positive linear relationship. A logistic model created using the maximum likelihood method was used for elucidating hook selectivity; the best fit model with the minimum Akaike’s Information Criterion value was selected as the final model. The 50% selection lengths were 224.827 and 233.179 mm for B. japonicus; 201.461 and 202.603 mm for D. tumifrons using “J” #13 and “J” #11 hooks, respectively. To preserve the reproductive potential of younger fish in the stocks, the size of the “J” #13 hook was selected as the minimum hook size that should be used for the sustainable development of bottom longline fishing for B. japonicus and D. tumifrons.