In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order t...In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.展开更多
There is a close relationship between potassium(K)and nitrogen(N).However,the roles of K under high N conditions remain unclear.Using a hydroponics approach,we monitored the morphological,physiological,and molecular c...There is a close relationship between potassium(K)and nitrogen(N).However,the roles of K under high N conditions remain unclear.Using a hydroponics approach,we monitored the morphological,physiological,and molecular changes in M9T337 apple(Malus domestica)rootstocks under different nitrate(10 and 30 mmol·L^(-1)NO_(3)^(-))and K supply(0.5,6,10,and 20 mmol·L_(-1)K^(+))conditions.Results revealed that high nitrate inhibited the root growth of M9T337 rootstocks,downregulated the expressions of K transporter genes(MdPT5,MdHKT1,and MdATK1),and reduced the net NO3-and K+influx at the surface of roots,thereby resulting in an N/K imbalance in rootstocks.Further investigation showed that 10 mmol·L^(-1)K increased the activity of N metabolic enzymes(NR,GS,NiR,and GOGAT),upregulated the expressions of genes related to nitrate uptake and transport(MdNRT1.1,MdNRT1.2,MdNRT1.5,and MdNRT2.4),promoted15N transport from the roots to the shoots,optimized leaf N distribution,and improved photosynthetic N utilization efficiency under high nitrate conditions.These results suggest that the negative effects of high nitrate may be related to the N/K imbalance and that reducing N/K in plants by increasing K supply level can effectively alleviate the inhibition of N assimilation by high nitrate stress.展开更多
基金supported by the Natural Science Foundation of Hunan Province of China(2022JJ30369)the Education Department Important Foundation of Hunan Province in China(23A0095)。
文摘In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.
基金supported by the Special Fund for the National Key R&D Program of China(Grant No.2023YFD2301000)the earmarked fund for CARS(Grant No.CARS-27)the Taishan Scholar Assistance Program from Shandong Provincial Government(Grant No.TSPD20181206)。
文摘There is a close relationship between potassium(K)and nitrogen(N).However,the roles of K under high N conditions remain unclear.Using a hydroponics approach,we monitored the morphological,physiological,and molecular changes in M9T337 apple(Malus domestica)rootstocks under different nitrate(10 and 30 mmol·L^(-1)NO_(3)^(-))and K supply(0.5,6,10,and 20 mmol·L_(-1)K^(+))conditions.Results revealed that high nitrate inhibited the root growth of M9T337 rootstocks,downregulated the expressions of K transporter genes(MdPT5,MdHKT1,and MdATK1),and reduced the net NO3-and K+influx at the surface of roots,thereby resulting in an N/K imbalance in rootstocks.Further investigation showed that 10 mmol·L^(-1)K increased the activity of N metabolic enzymes(NR,GS,NiR,and GOGAT),upregulated the expressions of genes related to nitrate uptake and transport(MdNRT1.1,MdNRT1.2,MdNRT1.5,and MdNRT2.4),promoted15N transport from the roots to the shoots,optimized leaf N distribution,and improved photosynthetic N utilization efficiency under high nitrate conditions.These results suggest that the negative effects of high nitrate may be related to the N/K imbalance and that reducing N/K in plants by increasing K supply level can effectively alleviate the inhibition of N assimilation by high nitrate stress.
