Weighted estimates for the integral operator with a logarithmic singularity

2016 ◽  
Author(s):  
Akbota Abylayeva
2010 ◽  
Vol 61 (3) ◽  
pp. 253-262
Author(s):  
Bohumír Opic ◽  
Jiří Rákosník

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Thabet Abdeljawad ◽  
Saima Rashid ◽  
A. A. El-Deeb ◽  
Zakia Hammouch ◽  
Yu-Ming Chu

Abstract The present work investigates the applicability and effectiveness of generalized proportional fractional integral ($\mathcal{GPFI}$ GPFI ) operator in another sense. We aim to derive novel weighted generalizations involving a family of positive functions n ($n\in \mathbb{N}$ n ∈ N ) for this recently proposed operator. As applications of this operator, we can generate notable outcomes for Riemann–Liouville ($\mathcal{RL}$ RL ) fractional, generalized $\mathcal{RL}$ RL -fractional operator, conformable fractional operator, Katugampola fractional integral operator, and Hadamard fractional integral operator by changing the domain. The proposed strategy is vivid, explicit, and it can be used to derive new solutions for various fractional differential equations applied in mathematical physics. Certain remarkable consequences of the main theorems are also figured.


1994 ◽  
Vol 1 (1) ◽  
pp. 77-97
Author(s):  
Luboš Pick

Abstract The aim of the present paper is to characterize the classes of weights which ensure the validity of one-weighted strong, weak or extra-weak type estimates in Orlicz classes for the integral operator


Author(s):  
Nguyen Minh Chuong ◽  
◽  
Dao Van Duong ◽  
Nguyen Duc Duyet ◽  
◽  
...  

2020 ◽  
pp. 1-10
Author(s):  
Brittany M. Stopa ◽  
Maya Harary ◽  
Ray Jhun ◽  
Arun Job ◽  
Saef Izzy ◽  
...  

OBJECTIVETraumatic brain injury (TBI) is a leading cause of morbidity and mortality in the US, but the true incidence of TBI is unknown.METHODSThe National Trauma Data Bank National Sample Program (NTDB NSP) was queried for 2007 and 2013, and population-based weighted estimates of TBI-related emergency department (ED) visits, hospitalizations, and deaths were calculated. These data were compared to the 2017 Centers for Disease Control and Prevention (CDC) report on TBI, which used the Healthcare Cost and Utilization Project’s National (“Nationwide” before 2012) Inpatient Sample and National Emergency Department Sample.RESULTSIn the NTDB NSP the incidence of TBI-related ED visits was 59/100,000 in 2007 and 62/100,000 in 2013. However, in the CDC report there were 534/100,000 in 2007 and 787/100,000 in 2013. The CDC estimate for ED visits was 805% higher in 2007 and 1169% higher in 2013. In the NTDB NSP, the incidence of TBI-related deaths was 5/100,000 in 2007 and 4/100,000 in 2013. In the CDC report, the incidence was 18/100,000 in both years. The CDC estimate for deaths was 260% higher in 2007 and 325% higher in 2013.CONCLUSIONSThe databases disagreed widely in their weighted estimates of TBI incidence: CDC estimates were consistently higher than NTDB NSP estimates, by an average of 448%. Although such a discrepancy may be intuitive, this is the first study to quantify the magnitude of disagreement between these databases. Given that research, funding, and policy decisions are made based on these estimates, there is a need for a more accurate estimate of the true national incidence of TBI.


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