{"id":"https://openalex.org/W2090546322","doi":"https://doi.org/10.1002/malq.200410043","title":"Some variations of the Hardy hierarchy","display_name":"Some variations of the Hardy hierarchy","publication_year":2005,"publication_date":"2005-06-08","ids":{"openalex":"https://openalex.org/W2090546322","doi":"https://doi.org/10.1002/malq.200410043","mag":"2090546322"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200410043","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410043","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078850482","display_name":"Henryk Kotlarski","orcid":null},"institutions":[{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"funder","lineage":["https://openalex.org/I99542240"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Henryk Kotlarski","raw_affiliation_strings":["Institute of Mathematics, Polish Academy of Sciences, ul. S\u0301niadeckich 8, 00 \u2013 950 Warszawa, Poland","Institute of Mathematics, Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-950 Warszawa, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Polish Academy of Sciences, ul. S\u0301niadeckich 8, 00 \u2013 950 Warszawa, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Institute of Mathematics, Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-950 Warszawa, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I4210137370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069785127","display_name":"Bo\u017cena Piekart","orcid":"https://orcid.org/0000-0002-6700-8117"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bo\u017cena Piekart","raw_affiliation_strings":["Instytut Matematyki i Fizyki, Akademia Podlaska, ul. 3 \u2013 go Maja 54, 08 \u2013 110 Siedlce, Poland"],"affiliations":[{"raw_affiliation_string":"Instytut Matematyki i Fizyki, Akademia Podlaska, ul. 3 \u2013 go Maja 54, 08 \u2013 110 Siedlce, Poland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078850482"],"corresponding_institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I99542240"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.4643,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62781587,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"51","issue":"4","first_page":"417","last_page":"434"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12812","display_name":"Meromorphic and Entire Functions","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12812","display_name":"Meromorphic and Entire Functions","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9333999752998352,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9052000045776367,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.8313515186309814},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.8072220087051392},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7699297070503235},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3805790841579437},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36401885747909546},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.052245527505874634}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.8313515186309814},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.8072220087051392},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7699297070503235},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3805790841579437},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36401885747909546},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.052245527505874634},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.200410043","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410043","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"MLQ","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W785447184","https://openalex.org/W1542740106","https://openalex.org/W1591170418","https://openalex.org/W1597834884","https://openalex.org/W1966414208","https://openalex.org/W1978312966","https://openalex.org/W1980915530","https://openalex.org/W2025460262","https://openalex.org/W2034362265","https://openalex.org/W2049321566","https://openalex.org/W2115737962","https://openalex.org/W2144092438","https://openalex.org/W2152101391","https://openalex.org/W2336574378"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1979597421","https://openalex.org/W1097487277","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2768610039","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694"],"abstract_inverted_index":{"We":[0],"study":[1],"some":[2],"variations":[3],"of":[4,12,23],"the":[5,18],"so-called":[6],"Hardy":[7],"hierarchy":[8],"(up":[9],"to":[10],"\u03b50)":[11],"quickly":[13],"growing":[14],"functions,":[15],"known":[16],"from":[17],"literature,":[19],"and":[20],"obtain":[21],"analogues":[22],"Ratajczyk's":[24],"approximation":[25],"lemma":[26],"for":[27],"them.":[28],"(\u00a9":[29],"2005":[30],"WILEY-VCH":[31],"Verlag":[32],"GmbH":[33],"&":[34],"Co.":[35],"KGaA,":[36],"Weinheim)":[37]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}