Answer by taking a quote from the following article:

Anton Friedrich Wilhelm (von) Webern (German: ['anton 've:ban] ( listen); 3 December 1883 - 15 September 1945) was an Austrian composer and conductor. Along with his mentor Arnold Schoenberg and his colleague Alban Berg, Webern was in the core of those in the circle of the Second Viennese School, including Ernst Krenek and Theodor W. Adorno. As an exponent of atonality and twelve-tone technique, Webern exerted influence on contemporaries Luigi Dallapiccola, Krenek, and even Schoenberg himself.

Webern insisted on lyricism, nuance, rubato, sensitivity, and both emotional and intellectual understanding in performance of music; this is evidenced by anecdotes, correspondence, extant recordings of Schubert's Deutsche Tanze (arr. Webern) and Berg's Violin Concerto under his direction, many such detailed markings in his scores, and finally by his compositional process as both publicly stated and later revealed in the musical and extramusical metaphors and associations everywhere throughout his sketches. As both a composer and conductor he was one of many (e.g., Wilhelm Furtwangler, Dimitri Mitropoulos, Hermann Scherchen) in a contemporaneous tradition of conscientiously and non-literally handling notated musical figures, phrases, and even entire scores so as to maximize expressivity in performance and to cultivate audience engagement and understanding.  This aspect of Webern's work had been typically missed in his immediate post-war reception, however, even as it may radically affect the music's reception. For example, Boulez's "complete" recording of Webern's music yielded more to this aesthetic the second time after largely missing it the first; but Eliahu Inbal's rendition of Webern's symphony with the hr-Sinfonieorchester is still far more within the spirit of the late Romantic performance tradition (which Webern seemingly intended for his music), nearly slowing to half-tempo for the whole of first movement and taking care to delineate and shape each melodic strand and expressive gesture throughout the entirety of the work.  Gunter Wand's 1966 recording of the Cantata No. 1 (1938-40), op. 29, with the Symphonieorchester des Bayerischen Rundfunks et al., may likewise be contrasted with both of Boulez's renditions.

Did anyone else have a style similar to his?
Boulez's "complete" recording of Webern's music