2024-03-29T08:28:50Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/695742022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116The Haar wavelets and the Haar scaling function in weighted $L^p$ spaces with $A_p^{\dy ,m}$ weightsIzuki, Mitsuoopen accessThe Haar waveletsthe Haar scaling functionweighted Lp spaceAdy,mp weightgreedy basis410The new class of weights called $A_p^{\dy ,m}$ weights is introduced. We prove that a characterization and an unconditional basis of the weighted $L^p$ space $L^p(\R^n , w(x)dx)$ with $w \in A_p^{\dy ,m}$ $(1<p<\infty)$ are given by the Haar wavelets and the Haar scaling function. As an application of these results, we establish a greedy basis by using the Haar wavelets and the Haar scaling function again.Department of Mathematics, Hokkaido University2006engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83916http://hdl.handle.net/2115/6957410.14943/83916Hokkaido University Preprint Series in Mathematics766125https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69574/1/pre766.pdfapplication/pdf111.46 KB2006