{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T22:58:16Z","timestamp":1725577096419},"publisher-location":"Basel","reference-count":38,"publisher":"Birkh\u00e4user Basel","isbn-type":[{"type":"print","value":"9783034601573"},{"type":"electronic","value":"9783034601580"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-0346-0158-0_18","type":"book-chapter","created":{"date-parts":[[2011,1,29]],"date-time":"2011-01-29T09:31:35Z","timestamp":1296293495000},"page":"321-336","source":"Crossref","is-referenced-by-count":3,"title":["Singular Integral Operators on Variable Lebesgue Spaces over Arbitrary Carleson Curves"],"prefix":"10.1007","author":[{"given":"Alexei Yu.","family":"Karlovich","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"18_CR1","volume-title":"Interpolation of Operators","author":"C. Bennett","year":"1988","unstructured":"C. Bennett and R. Sharpley, Interpolation of Operators. Academic Press, Boston, 1988."},{"key":"18_CR2","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/978-3-0348-9040-3_4","volume":"90","author":"A. B\u00f6ttcher","year":"1996","unstructured":"A. B\u00f6ttcher and Yu.I. Karlovich, Toeplitz and singular integral operators on general Carleson Jordan curves. In: \u201cSingular integral operators and related topics (Tel Aviv, 1995)\u201d. Operator Theory: Advances and Applications 90 (1996), 119\u2013152.","journal-title":"\u201cSingular integral operators and related topics (Tel Aviv, 1995)\u201d. Operator Theory: Advances and Applications"},{"key":"18_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8922-3","volume-title":"Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators","author":"A. B\u00f6ttcher","year":"1997","unstructured":"A. B\u00f6ttcher and Yu.I. Karlovich, Carleson Curves, Muckenhoupt Weights, and Toeplitz Operators. Birkh\u00e4user, Basel, 1997."},{"key":"18_CR4","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/978-3-0348-8362-7_5","volume":"129","author":"A. B\u00f6ttcher","year":"2001","unstructured":"A. B\u00f6ttcher and Yu.I. Karlovich, Cauchy\u2019s singular integral operator and its beautiful spectrum. In: \u201cSystems, approximation, singular integral operators, and related topics\u201d. Operator Theory: Advances and Applications 129 (2001), 109\u2013142.","journal-title":"\u201cSystems, approximation, singular integral operators, and related topics\u201d. Operator Theory: Advances and Applications"},{"key":"18_CR5","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1007\/BF01203026","volume":"25","author":"A. B\u00f6ttcher","year":"1996","unstructured":"A. B\u00f6ttcher, Yu.I. Karlovich, and V.S. Rabinovich, Emergence, persistence, and disappearance of logarithmic spirals in the spectra of singular integral operators. Integral Equations Operator Theory 25 (1996), 406\u2013444.","journal-title":"Integral Equations Operator Theory"},{"key":"18_CR6","first-page":"171","volume":"43","author":"A. B\u00f6ttcher","year":"2000","unstructured":"A. B\u00f6ttcher, Yu.I. Karlovich, and V.S. Rabinovich, The method of limit operators for one-dimensional singular integrals with slowly oscillating data. J. Operator Theory 43 (2000), 171\u2013198.","journal-title":"J. Operator Theory"},{"key":"18_CR7","volume-title":"Analysis of Toeplitz Operators","author":"A. B\u00f6ttcher","year":"2006","unstructured":"A. B\u00f6ttcher and B. Silbermann, Analysis of Toeplitz Operators. 2nd edition. Springer-Verlag, Berlin, 2006.","edition":"2nd edition"},{"key":"18_CR8","volume-title":"Operator Theory: Advances and Applications","author":"K.P. Clancey","year":"1981","unstructured":"K.P. Clancey and I. Gohberg, Factorization of Matrix Functions and Singular Integral Operators. Operator Theory: Advances and Applications 3. Birkh\u00e4user, Basel, 1981."},{"key":"18_CR9","doi-asserted-by":"crossref","first-page":"157","DOI":"10.24033\/asens.1469","volume":"17","author":"G. David","year":"1984","unstructured":"G. David, Oper\u00e1teurs int\u00e9graux singuliers sur certaines courbes du plan complexe. Ann. Sci. \u00c9cole Norm. Super. 17 (1984), 157\u2013189.","journal-title":"Ann. Sci. \u00c9cole Norm. Super."},{"key":"18_CR10","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1002\/mana.19931620114","volume":"162","author":"T. Finck","year":"1993","unstructured":"T. Finck, S. Roch, and B. Silbermann, Two projections theorems and symbol calculus for operators with massive local spectra. Math. Nachr. 162 (1993), 167\u2013185.","journal-title":"Math. Nachr."},{"key":"18_CR11","doi-asserted-by":"crossref","first-page":"347","DOI":"10.4064\/sm-31-4-347-362","volume":"31","author":"I.C. Gohberg","year":"1968","unstructured":"I.C. Gohberg and N.Ya. Krupnik, The spectrum of singular integral operators in L p spaces. Studia Math. 31 (1968), 347\u2013362 (in Russian).","journal-title":"Studia Math."},{"key":"18_CR12","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1070\/IM1971v005n04ABEH001127","volume":"5","author":"I. Gohberg","year":"1971","unstructured":"I. Gohberg and N. Krupnik, Singular integral operators with piecewise continuous coefficients and their symbols. Math. USSR Izvestiya 5 (1971), 955\u2013979.","journal-title":"Math. USSR Izvestiya"},{"key":"18_CR13","volume-title":"Operator Theory: Advances and Applications","author":"I. Gohberg","year":"1992","unstructured":"I. Gohberg and N. Krupnik, One-Dimensional Linear Singular Integral Equations. Vols. 1 and 2. Operator Theory: Advances and Applications53\u201354. Birkh\u00e4user, Basel, 1992."},{"key":"18_CR14","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1007\/BF01205291","volume":"16","author":"I. Gohberg","year":"1993","unstructured":"I. Gohberg and N. Krupnik, Extension theorems for Fredholm and invertibility symbols. Integral Equations Operator Theory 16 (1993), 514\u2013529.","journal-title":"Integral Equations Operator Theory"},{"key":"18_CR15","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1007\/BF01194990","volume":"32","author":"A. Yu. Karlovich","year":"1998","unstructured":"A. Yu. Karlovich, Singular integral operators with piecewise continuous coefficients in reflexive rearrangement-invariant spaces. Integral Equations Operator Theory 32 (1998), 436\u2013481.","journal-title":"Integral Equations Operator Theory"},{"key":"18_CR16","first-page":"303","volume":"47","author":"A.Yu. Karlovich","year":"2002","unstructured":"A.Yu. Karlovich, Algebras of singular integral operators with PC coefficients in rearrangement-invariant spaces with Muckenhoupt weights. J. Operator Theory 47 (2002), 303\u2013323.","journal-title":"J. Operator Theory"},{"key":"18_CR17","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1216\/jiea\/1181074970","volume":"15","author":"A.Yu. Karlovich","year":"2003","unstructured":"A.Yu. Karlovich, Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces. J. Integr. Equat. Appl. 15 (2003), 263\u2013320.","journal-title":"J. Integr. Equat. Appl."},{"key":"18_CR18","unstructured":"A.Yu. Karlovich, Algebras of singular integral operators on Nakano spaces with Khvedelidze weights over Carleson curves with logarithmic whirl points. In: \u201cPseudodifferential Equations and Some Problems of Mathematical Physics\u201d, Rostov-on-Don, 2005, 135\u2013142. Preprint is available at arXiv:math\/0507312."},{"key":"18_CR19","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/978-3-7643-7980-3_9","volume":"171","author":"A.Yu. Karlovich","year":"2006","unstructured":"A.Yu. Karlovich, Algebras of singular integral operators with piecewise continuous coefficients on weighted Nakano spaces. In: \u201cThe Extended Field of Operator Theory\u201d. Operator Theory: Advances and Applications 171 (2006), 171\u2013188.","journal-title":"The Extended Field of Operator Theory\u201d. Operator Theory: Advances and Applications"},{"key":"18_CR20","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/978-3-0346-0174-0_9","volume":"195","author":"A.Yu. Karlovich","year":"2009","unstructured":"A.Yu. Karlovich, Singular integral operators on variable Lebesgue spaces with radial oscillating weights. In: Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications 195 (2009), 185\u2013212.","journal-title":"Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications"},{"key":"18_CR21","unstructured":"A.Yu. Karlovich, Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves. Math. Nachr., to appear. Preprint is available at arXiv:0808.0258."},{"key":"18_CR22","first-page":"167","volume":"170","author":"V. Kokilashvili","year":"2006","unstructured":"V. Kokilashvili, V. Paatashvili, and S. Samko, Boundedness in Lebesgue spaces with variable exponent of the Cauchy singular operator on Carleson curves. In: \u201cModern Operator Theory and Applications. The Igor Borisovich Simonenko Anniversary Volume\u201d. Operator Theory: Advances and Applications 170 (2006), 167\u2013186.","journal-title":"\u201cModern Operator Theory and Applications. The Igor Borisovich Simonenko Anniversary Volume\u201d. Operator Theory: Advances and Applications"},{"key":"18_CR23","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1155\/2007\/914143","volume":"5","author":"V. Kokilashvili","year":"2007","unstructured":"V. Kokilashvili, N. Samko, and S. Samko, The maximal operator in weighted variable spaces L p(\u00b7). J. Funct. Spaces Appl. 5 (2007), 299\u2013317.","journal-title":"J. Funct. Spaces Appl."},{"key":"18_CR24","doi-asserted-by":"publisher","first-page":"1145","DOI":"10.1002\/mana.200510542","volume":"280","author":"V. Kokilashvili","year":"2007","unstructured":"V. Kokilashvili, N. Samko, and S. Samko, Singular operators in variable spaces L p(\u00b7) (\u03a9, \u03c1) with oscillating weights. Math. Nachr. 280 (2007), 1145\u20131156.","journal-title":"Math. Nachr."},{"key":"18_CR25","first-page":"61","volume":"131","author":"V. Kokilashvili","year":"2003","unstructured":"V. Kokilashvili and S. Samko, Singular integral equations in the Lebesgue spaces with variable exponent. Proc. A. Razmadze Math. Inst. 131 (2003), 61\u201378.","journal-title":"Proc. A. Razmadze Math. Inst."},{"key":"18_CR26","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/j.jmaa.2008.06.056","volume":"352","author":"V. Kokilashvili","year":"2009","unstructured":"V. Kokilashvili and S. Samko, Operators of harmonic analysis in weighted spaces with non-standard growth. J. Math. Anal. Appl. 352 (2009), 15\u201334.","journal-title":"J. Math. Anal. Appl."},{"issue":"116","key":"18_CR27","doi-asserted-by":"crossref","first-page":"592","DOI":"10.21136\/CMJ.1991.102493","volume":"41","author":"O. Kov\u00e1\u010dik","year":"1991","unstructured":"O. Kov\u00e1\u010dik and J. R\u00e1kosn\u00edk, On spaces L p(x) and W k,p(x) . Czechoslovak Math. J. 41(116) (1991), 592\u2013618.","journal-title":"Czechoslovak Math. J."},{"key":"18_CR28","unstructured":"S.G. Krein, Ju.I. Petunin, and E.M. Semenov, Interpolation of Linear Operators. AMS Translations of Mathematical Monographs 54, Providence, RI, 1982."},{"key":"18_CR29","volume-title":"Operator Theory: Advances and Applications","author":"G.S. Litvinchuk","year":"1987","unstructured":"G.S. Litvinchuk and I.M. Spitkovsky, Factorization of Measurable Matrix Functions. Operator Theory: Advances and Applications 25. Birkh\u00e4user, Basel, 1987."},{"key":"18_CR30","volume-title":"Lecture Notes in Mathematics","author":"J. Musielak","year":"1983","unstructured":"J. Musielak, Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics 1034. Springer-Verlag, Berlin, 1983."},{"key":"18_CR31","volume-title":"Modulared Semi-Ordered Linear Spaces","author":"H. Nakano","year":"1950","unstructured":"H. Nakano, Modulared Semi-Ordered Linear Spaces. Maruzen Co., Ltd., Tokyo, 1950."},{"key":"18_CR32","doi-asserted-by":"publisher","first-page":"1261","DOI":"10.1070\/IM1996v060n06ABEH000099","volume":"60","author":"V.S. Rabinovich","year":"1996","unstructured":"V.S. Rabinovich, Algebras of singular integral operators on composed contours with nodes that are logarithmic whirl points. Izvestiya Mathematics 60 (1996), 1261\u20131292.","journal-title":"Izvestiya Mathematics"},{"key":"18_CR33","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/s00020-008-1566-9","volume":"60","author":"V. Rabinovich","year":"2008","unstructured":"V. Rabinovich and S. Samko, Boundedness and Fredholmness of pseudodifferential operators in variable exponent spaces. Integral Equations Operator Theory 60 (2008), 507\u2013537.","journal-title":"Integral Equations Operator Theory"},{"key":"18_CR34","first-page":"277","volume":"28","author":"I.B. Simonenko","year":"1964","unstructured":"I.B. Simonenko, The Riemann boundary value problem for n pairs functions with measurable coefficients and its application to the investigation of singular integral operators in the spaces L p with weight. Izv. Akad. Nauk SSSR, Ser. Matem. 28 (1964), 277\u2013306 (in Russian).","journal-title":"Izv. Akad. Nauk SSSR, Ser. Matem."},{"key":"18_CR35","first-page":"567","volume":"29","author":"I.B. Simonenko","year":"1965","unstructured":"I.B. Simonenko, A new general method of investigating linear operator equations of singular integral equations type. Izv. Akad. Nauk SSSR, Ser. Matem. 29 (1965), part I: 567\u2013586","journal-title":"Izv. Akad. Nauk SSSR, Ser. Matem."},{"key":"18_CR36","doi-asserted-by":"publisher","first-page":"1091","DOI":"10.1070\/IM1968v002n05ABEH000706","volume":"2","author":"I.B. Simonenko","year":"1968","unstructured":"I.B. Simonenko, Some general questions in the theory of the Riemann boundary value problem. Math. USSR Izvestiya 2 (1968), 1091\u20131099.","journal-title":"Math. USSR Izvestiya"},{"key":"18_CR37","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/0022-1236(92)90075-T","volume":"105","author":"I.M. Spitkovsky","year":"1992","unstructured":"I.M. Spitkovsky, Singular integral operators with PC symbols on the spaces with general weights. J. Funct. Anal. 105 (1992), 129\u2013143.","journal-title":"J. Funct. Anal."},{"key":"18_CR38","first-page":"131","volume":"97","author":"H. Widom","year":"1960","unstructured":"H. Widom, Singular integral equations on L p . Trans. Amer. Math. Soc. 97 (1960), 131\u2013160.","journal-title":"Trans. Amer. Math. Soc."}],"container-title":["Topics in Operator Theory"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-0346-0158-0_18.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T02:59:36Z","timestamp":1637204376000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-0346-0158-0_18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783034601573","9783034601580"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-0346-0158-0_18","relation":{},"subject":[],"published":{"date-parts":[[2010]]}}}