Geodesic
Two-sided estimates of the $K$-functional for spaces of functions of generalized bounded variation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 1, pp. 26-36

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A two-sided estimate is proposed for the $K$-functional of the pair $(C[0,1], BV(X))$, where $BV(X)$ is the space of functions of generalized bounded variation constructed from a symmetric sequence space $X$. The application of this estimate to various sequence spaces $X$ yields new interpolation theorems for spaces of finite Wiener–Young $h$-variation, of finite Waterman $\Lambda$-variation, of bounded modulus of variation in the sense of Chanturiya, etc.
Keywords: space of functions of generalized bounded variation, $K$-functional, real interpolation method. 
@article{FAA_2022_56_1_a1,
     author = {E. I. Berezhnoi},
     title = {Two-sided estimates of the $K$-functional for spaces of functions of generalized bounded variation},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {26--36},
     publisher = {mathdoc},
     volume = {56},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_1_a1/}
}
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E. I. Berezhnoi. Two-sided estimates of the $K$-functional for spaces of functions of generalized bounded variation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 1, pp. 26-36. http://geodesic.mathdoc.fr/item/FAA_2022_56_1_a1/