The　almost　everywhere　convergence　of　wavelet　series　is　important　in　wavelet　analysis　[S.　Kelly,　M.A.　Kon,　L.A.　Raphael,　Local　convergence　for　wavelet　expansions,　J.　Funct.　Anal.　126　(1994)　102-138].　Since　the　thresholding　method　plays　fundamental　roles　in　data　compression,　signal　processing　and　other　areas,　the　pointwise　convergence　of　resulting　wavelet　series　was　investigated　by　T.　Tao　and　B.　Vidakovic　in　1996　and　2000.　Chen　and　Meng　study　the　same　problem　for　differential　operators　in　L-p(R)　setting　[Di-Rong　Chen,　Hong-Tao　Meng,　Convergence　of　wavelet　thresholding　estimators　of　differential　operators,　Appl.　Comput.　Harmon.　Anal.　25　(2008)　266-275].　This　paper　deals　with　the　uniform　and　norm　convergence　of　wavelet　thresholding　estimator　of　differential　operators　on　Besov　spaces　and　Sobolev　spaces　with　integer　exponents.　In　particular,　the　convergence　order　is　focused.　To　do　that,　we　first　study　the　corresponding　problems　for　non-standard　forms　of　those　operators.　Crown　Copyright　(C)　2011　Published　by　Elsevier　Inc.　All　rights　reserved.