{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T18:17:04Z","timestamp":1775413024124,"version":"3.50.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1975,1,1]],"date-time":"1975-01-01T00:00:00Z","timestamp":157766400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1975,1,1]],"date-time":"1975-01-01T00:00:00Z","timestamp":157766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sib Math J"],"published-print":{"date-parts":[[1975,1]]},"DOI":"10.1007\/bf00967460","type":"journal-article","created":{"date-parts":[[2005,1,12]],"date-time":"2005-01-12T02:14:50Z","timestamp":1105496090000},"page":"35-48","source":"Crossref","is-referenced-by-count":4,"title":["Singular convolution operators with a discontinuous symbol"],"prefix":"10.1007","volume":"16","author":[{"given":"N. K.","family":"Karapetyants","sequence":"first","affiliation":[]},{"given":"S. G.","family":"Samko","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF00967460_CR1","volume-title":"Boundary Value Problems","author":"F. D. Gakhov","year":"1963","unstructured":"F. D. Gakhov, Boundary Value Problems [in Russian], Fizmatgiz, Moscow (1963)."},{"key":"BF00967460_CR2","volume-title":"Singular Integral Equations","author":"N. I. Muskhelishvili","year":"1968","unstructured":"N. I. Muskhelishvili, Singular Integral Equations [in Russian], Nauka, Moscow (1968)."},{"issue":"No. 3","key":"BF00967460_CR3","first-page":"504","volume":"194","author":"N. K. Karapetyants","year":"1970","unstructured":"N. K. Karapetyants and S. G. Samko, \u201cOn the index of certain classes of integral operators,\u201d Dokl. Akad. Nauk SSSR,194, No. 3, 504\u2013507 (1970).","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"No. 1","key":"BF00967460_CR4","first-page":"26","volume":"8","author":"N. K. Karapetyants","year":"1973","unstructured":"N. K. Karapetyants and S. G. Samko, \u201cOn the index of certain classes of integral operators,\u201d Izv. Akad. Nauk ArmSSR, Ser. Matem.,8, No. 1, 26\u201340 (1973).","journal-title":"Izv. Akad. Nauk ArmSSR, Ser. Matem."},{"key":"BF00967460_CR5","first-page":"3","volume":"168","author":"G. I. Savel'ev","year":"1960","unstructured":"G. I. Savel'ev, \u201cOn a class of linear singular integral equations,\u201d Trudy Novocherkassk. Politekh. Inst.,168, 3\u201310 (1960).","journal-title":"Trudy Novocherkassk. Politekh. Inst."},{"issue":"No. 1","key":"BF00967460_CR6","first-page":"17","volume":"67","author":"R. V. Duduchaea","year":"1972","unstructured":"R. V. Duduchaea, \u201cDiscrete Wiener-Hopf equations in the spacel\np with a weight,\u201d Soob. Akad. Nauk GSSR,67, No. 1, 17\u201320 (1972).","journal-title":"Soob. Akad. Nauk GSSR"},{"issue":"No. 3","key":"BF00967460_CR7","first-page":"714","volume":"35","author":"N. K. Karapetyants","year":"1971","unstructured":"N. K. Karapetyants and S. G. Samko, \u201cOn a class of convolution type integral equations, and its applications,\u201d Izv. Akad. Nauk SSSR, Ser. Matem.,35, No. 3, 714\u2013726 (1971).","journal-title":"Izv. Akad. Nauk SSSR, Ser. Matem."},{"key":"BF00967460_CR8","volume-title":"Integral Operators in Spaces of Summable Functions","author":"M. A. Krasnosel'skii","year":"1966","unstructured":"M. A. Krasnosel'skii, P. P. Zabreiko, E. I. Pustyl'nik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions [in Russian], Nauka, Moscow (1966)."},{"issue":"No. 3","key":"BF00967460_CR9","first-page":"29","volume":"111","author":"S. G. Mikhlin","year":"1948","unstructured":"S. G. Mikhlin, \u201cSingular int\u00e8gral equations,\u201d Usp. Matem. Nauk.111, No. 3, 29\u2013112 (1948).","journal-title":"Usp. Matem. Nauk."},{"key":"BF00967460_CR10","unstructured":"T. Carleman, L'int\u00e8grale de Fourier et questions qui se rattachent, Uppsala (1944)."},{"key":"BF00967460_CR11","volume-title":"Inequalities","author":"G. Hardy","year":"1948","unstructured":"G. Hardy, J. Littlewood, and G. Polya, Inequalities [Russian translation], IL, Moscow (1948)."},{"key":"BF00967460_CR12","first-page":"160","volume":"50","author":"H. Kober","year":"1941","unstructured":"H. Kober, \u201cOn a theory of Schur and on fractional integrals of purely imaginary order,\u201d Trans. Amer. Math. Soc.,50, 160\u2013174 (1941).","journal-title":"Trans. Amer. Math. Soc."},{"issue":"No. 2","key":"BF00967460_CR13","doi-asserted-by":"crossref","first-page":"452","DOI":"10.2307\/2373387","volume":"93","author":"M. J. Fisher","year":"1971","unstructured":"M. J. Fisher, \u201cPurely imaginary powers of certain differential operators. I,\u201d Amer. J. Math.,93, No. 2, 452\u2013478 (1971).","journal-title":"Amer. J. Math."},{"issue":"No. 3","key":"BF00967460_CR14","first-page":"325","volume":"60","author":"P. I. Lizorkin","year":"1963","unstructured":"P. I. Lizorkin, \u201cGeneralized Liouville differentiation and the functional spaces Lrp(En). Embedding theorems,\u201d Matem. Sb.,60, No. 3, 325\u2013352 (1963).","journal-title":"Matem. Sb."},{"key":"BF00967460_CR15","first-page":"89","volume":"105","author":"P. I. Lizorkin","year":"1969","unstructured":"P. I. Lizorkin, \u201cGeneralized Liouville differentiation and the method of multipliers in the embedding theory of classes of differentiable functions,\u201d Trudy Matem. Inst. Akad. Nauk SSSR,105, 89\u2013167 (1969).","journal-title":"Trudy Matem. Inst. Akad. Nauk SSSR"},{"key":"BF00967460_CR16","volume-title":"Spaces of Generalized Functions","author":"I. M. Gel'fand","year":"1958","unstructured":"I. M. Gel'fand and G. E. Shilov, Spaces of Generalized Functions [in Russian], Fizmatgiz, Moscow (1958)."},{"key":"BF00967460_CR17","volume-title":"Generalized Functions and Operations","author":"I. M. Gel'fand","year":"1959","unstructured":"I. M. Gel'fand and G. E. Shilov, Generalized Functions and Operations [in Russian], Fizmatgiz, Moscow (1959)."},{"key":"BF00967460_CR18","first-page":"385","volume":"XI","author":"M. Arosajn","year":"1961","unstructured":"M. Arosajn and K. Smith, \u201cTheory of Bessel potentials. I,\u201d Ann. Inst. Fourier,XI, 385\u2013475 (1961).","journal-title":"Ann. Inst. Fourier"},{"key":"BF00967460_CR19","first-page":"337","volume":"6","author":"A. Marchaud","year":"1927","unstructured":"A. Marchaud, \u201cSur les deriv\u00e8es et sur les differences des fonctions,\u201d J. Math. Pures Appl.,6, 337\u2013425 (1927).","journal-title":"J. Math. Pures Appl."},{"issue":"No. 5","key":"BF00967460_CR20","first-page":"359","volume":"8","author":"S. G. Samko","year":"1973","unstructured":"S. G. Samko, \u201cOn the space I\u03b1(Lp) of fractional integrals and on potential type operators,\u201d Izv. Akad. Nauk ArmSSR, Ser. Matem.,8, No. 5, 359\u2013383 (1973).","journal-title":"Izv. Akad. Nauk ArmSSR, Ser. Matem."},{"key":"BF00967460_CR21","first-page":"175","volume-title":"Mathematical Analysis and Its Applications","author":"S. G. Samko","year":"1969","unstructured":"S. G. Samko, \u201cOn the integral modulus of continuity of potentials with densities that are summable on the real line with a weight,\u201d in: Mathematical Analysis and Its Applications [in Russian], Izd. Rostov Univ., Rostov-on-Don (1969), pp. 175\u2013184."},{"key":"BF00967460_CR22","volume-title":"Multidimensional Singular Integrals and Integral Equations","author":"S. G. Mikhlin","year":"1962","unstructured":"S. G. Mikhlin Multidimensional Singular Integrals and Integral Equations [in Russian], Fizmatgiz, Moscow (1962)."},{"key":"BF00967460_CR23","volume-title":"Introduction to the Theory of One-Dimentional Singular Integral Operators","author":"I. Ts. Gokhberg","year":"1973","unstructured":"I. Ts. Gokhberg and N. Ya. Krupnik, Introduction to the Theory of One-Dimentional Singular Integral Operators [in Russian], Shtiintsa, Kishinev (1973)."},{"key":"BF00967460_CR24","volume-title":"The Theory of Noetherian Operators","author":"V. S. Rogozhin","year":"1973","unstructured":"V. S. Rogozhin, The Theory of Noetherian Operators [in Russian], Izd. Rostov Univ., Rostov-on-Don (1973)."},{"issue":"No. 1","key":"BF00967460_CR25","first-page":"17","volume":"200","author":"N. K. Karapetyants","year":"1971","unstructured":"N. K. Karapetyants and S. G. Samko, \u201cOn discrete Wiener-Hopf operators with oscillatory coefficients,\u201d Dokl. Akad. Nauk SSSR,200, No. 1, 17\u201321 (1971).","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"No. 5","key":"BF00967460_CR26","first-page":"1138","volume":"32","author":"I. B. Simonenko","year":"1968","unstructured":"I. B. Simonenko, \u201cSome general questions about the theory of the Riemann boundary value problem,\u201d Izv. Akad. Nauk SSSR, Ser. Matem.,32, No. 5, 1138\u20131146 (1968).","journal-title":"Izv. Akad. Nauk SSSR, Ser. Matem."},{"issue":"No. 1","key":"BF00967460_CR27","first-page":"131","volume":"97","author":"H. Widom","year":"1960","unstructured":"H. Widom, \u201cSingular integral equations in Lp,\u201d Trans. Amer. Math. Soc.,97, No. 1, 131\u2013160 (1960).","journal-title":"Trans. Amer. Math. Soc."},{"key":"BF00967460_CR28","volume-title":"Convolution Equations and Projection Methods of Solving Them","author":"I. Ts. Gokhberg","year":"1971","unstructured":"I. Ts. Gokhberg and I. A. Fel'dman, Convolution Equations and Projection Methods of Solving Them [in Russian], Nauka, Moscow (1971)."},{"key":"BF00967460_CR29","volume-title":"Tables of Integrals, Sums, Series, and Products","author":"I. S. Gradshtein","year":"1962","unstructured":"I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Ed. 4, Fizmatgiz, Moscow (1962).","edition":"Ed. 4"},{"issue":"No. 4","key":"BF00967460_CR30","doi-asserted-by":"crossref","first-page":"347","DOI":"10.4064\/sm-31-4-347-362","volume":"31","author":"I. Ts. Gokhberg","year":"1968","unstructured":"I. Ts. Gokhberg and N. Ya. Krupnik, \u201cOn the spectrum of singular integral operators in the Lp space,\u201d Studia Math.,31, No. 4, 347\u2013362 (1968).","journal-title":"Studia Math."},{"issue":"No. 5","key":"BF00967460_CR31","first-page":"373","volume":"7","author":"B. S. Rubin","year":"1972","unstructured":"B. S. Rubin, \u201cOn the spaces of fractional integrals on a rectilinear contour,\u201d Izv. Akad. Nauk ArmSSR, Ser. Matem.,7, No. 5, 373\u2013386 (1972).","journal-title":"Izv. Akad. Nauk ArmSSR, Ser. Matem."},{"key":"BF00967460_CR32","volume-title":"Estimates for Operators Invariant under a Shift","author":"L. H\u00f6rmander","year":"1962","unstructured":"L. H\u00f6rmander, Estimates for Operators Invariant under a Shift [Russian translation], IL, Moscow (1962)."}],"container-title":["Siberian Mathematical Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00967460.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/BF00967460","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00967460","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00967460.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T16:45:29Z","timestamp":1775407529000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/BF00967460"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1975,1]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1975,1]]}},"alternative-id":["BF00967460"],"URL":"https:\/\/doi.org\/10.1007\/bf00967460","relation":{},"ISSN":["0037-4466","1573-9260"],"issn-type":[{"value":"0037-4466","type":"print"},{"value":"1573-9260","type":"electronic"}],"subject":[],"published":{"date-parts":[[1975,1]]}}}