Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (Lq(),lp())(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.
This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.
In this paper, we investigate a 1D pressureless Euler-alignment system with a non-local alignment term, describing a kind of self-organizing problem for flocking. As a result, by the transport equation theory and Lagrange coordinate transformation, the local well-posedness of the solutions for the 1D pressureless Euler-alignment in Besov spaces with 1≤p∞ is established. Next, the ill-posedness of the solutions for this model in Besov spaces with 1≤p and is also deduced. Finally, the precise blow-up criteria of the solutions for this system is presented in Besov spaces with 1≤p .
We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.
The Republic of Korea has the highest suicide rate of older population among OECD countries,and depression is the prevailing factor.While it is well-known that the urban physical environment affects mental health,research on the physical characteristics of spaces remains limited.This study aims to explore relationship-oriented space characteristics that can form social networks and reduce depressive symptoms in older adults.After analyzing the differences in social interaction spaces between high-density and low-density areas for older adults in Seoul,we identified social interaction spaces(parks and traditional markets)that are frequently used based on on-site interview results.Two areas were selected for the questionnaire surveys.The main findings revealed that older adults living in areas with diverse spatial planning and close physical relationships between parks and traditional markets,convenient pedestrian environments,and lower population density of older adults had better social networks and lower depressive symptoms.More significantly,the physical characteristics of parks and traditional markets(convenient accessibility,maximized visibility,connectivity,and territoriality)significantly facilitate social interactions.Those engaging in social interactions within these spaces exhibited significantly better social networks and lower depressive symptoms.These findings underscore the importance of considering relationship-oriented space characteristics in spatial and urban planning.
