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On embeddings between spaces of functions of generalized bounded variation. (arXiv:1802.01726v1 [math.FA])
来源于:arXiv
In this note, we aim to establish a number of embeddings between various
function spaces that are frequently considered in the theory of Fourier series.
More specifically, we give sufficient conditions for the embeddings $\Phi
V[h]\subseteq \Lambda\text{BV}^{(p_n\uparrow p)}$, $\Lambda
V[h_1]^{(p)}\subseteq\Gamma V[h_2]^{(q)}$ and $\Lambda\text{BV}^{(p_n\uparrow
p)}\subseteq\Gamma\text{BV}^{(q_n\uparrow q)}$. Our results are new even for
the well-known spaces that have been studied in the literature. In particular,
a number of results due to M. Avdispahi\'{c}, that describe relationships
between the classes $\Lambda\text{BV}$ and $V[h]$, are derived as special
cases. 查看全文>>