Continuity of generalized Riesz potentials for double phase functionals with variable exponents

In this note, we discuss the continuity of generalized Riesz potentials ( I_{rho}f) of functions in Morrey spaces (L^{Phi,nu(cdot)}(G)) of double phase functionals with variable exponents

Hardy-Sobolev inequalities in the half space (Theory of function spaces and related topics)

Our aim is to establish Hardy-Sobolev inequalities for Sobolev functions in Herz-Morrey spaces, which extend the classical Hardy inequalities in the L[p] Lebesgue space

Boundedness of generalized fractional integral operators on Orlicz spaces near L1L^1 over metric measure spaces

summary:We are concerned with the boundedness of generalized fractional integral operators $I_{\rho ,\tau }$ from Orlicz spaces $L^{\Phi }(X)$ near $L^1(X)$ to Orlicz spaces $L^{\Psi }(X)$ over metric measure spaces equipped with lower Ahlfors $Q$-regular measures, where $\Phi$ is a function of the form $\Phi (r)=r\ell (r)$ and $\ell$ is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials

On Trudinger-type inequalities in Orlicz-Morrey spaces of an integral form

We give Trudinger-type inequalities for Riesz potentials of functions in Orlicz-Morrey spaces of an integral formover non-doublingmetricmeasure spaces. Our results are new even for the doubling metric measure setting. In particular, our results improve and extend the previous results in Morrey spaces of an integral form in the Euclidean case.Peer reviewe

Intermittent Beginning to the Formation of Hydrogenous Ferromanganese Nodules in the Vast Field: Insights from Multi-Element Chemostratigraphy Using Microfocus X-ray Fluorescence

南極からの海洋深層水が「国産コバルト資源」を生み出した --南鳥島周辺に広大なマンガンノジュール密集域が形成された原因を特定--. 京都大学プレスリリース. 2022-01-12.Vast ferromanganese nodule fields have been found on the deep-sea floor of all oceans worldwide. They have received attention because they potentially provide high-grade metal resources to develop future high- and green-technology. However, how these vast nodule fields were formed and developed owing to their widespread nature or tendency to be denser with an increasing number of nodules has not yet been established. In this study, the fine-scale inner structure of nodules of various sizes was analyzed on the basis of chemical mapping using microfocus X-ray fluorescence. We found that nodules distributed in the vast field around Minamitorishima (Marcus) Island have several types of innermost layers, which correspond to different chemostratigraphic layers of nodules that have been previously reported by us in this region. As nodules grow in order from the center to the outside, the different types in the innermost layer indicate a difference in the timing of the beginning of their growth. Moreover, because the differences in the chemical features of each layer reflect differences in the composition of the original deep-sea water, our results imply that the beginning of nodule formation occurred intermittently at each time of a water mass replacement due to new deep-sea currents flowing into this region. We recognized that the northern part of the study area was dominated by large nodules that started to grow in relatively earlier times, while the southern part tended to have many nodules that grew in relatively later times. Based on these observations, we hypothesize that the intermittent beginning of nodule formation is governed by the northward inflow of the deep-sea current that originated from the Lower Circumpolar Deep Water for an extended time to form the vast nodule field. Because patterns in the timing of nodule formation were different in the eastern and western regions, we thus further propose that the topographic framework, i.e., the arrangement of individual large seamounts and the cluster of small knolls and petit-spot volcanoes, strongly regulates the flow path of the deep-sea current, even if the position of the entire seamount changes owing to plate motion. The deep-sea current might supply some materials to be nuclei, resulting in the nodule formation at the beginning of the process