Boundedness of the wavelet integral operator on weighted function spaces

Besov norms in terms of the S-transform

“…We give the definitions of weighted Besov spaces [1] associated with a temperate weight function and obtain boundedness results for S ω .…”

“…In this section we recall the definitions of Besov spaces due to Peetre [4] and obtain the boundedness results for S-transform on Besov spaces analogous to the boundedness results for wavelet transform on Besov spaces [1,5]. Definition 3.1 For f ∈ L p (R) and for any fixed η ∈ R, we write…”

Certain properties of continuous fractional wavelet transform on Hardy space and Morrey space

“…WT has also been studied in various function spaces and the spaces of distributions ( [25], [17], [19]). Chuong et al [5] studied the boundedness of the WT on the Besov, BMO and Hardy spaces. Furthermore, for the compactly supported basic wavelet, the boundedness of the WT is also established on the weighted Besov space and weighted BMO space associated with the tempered weight function.…”