Java hashCode() - Revision history

en>Cydebot: Robot - Speedily moving category Java programming language to :Category:Java (programming language) per CFDS.

2014-12-11T01:19:21Z

Robot - Speedily moving category Java programming language to Category:Java (programming language) per CFDS.

← Older revision		Revision as of 03:19, 11 December 2014
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	~~The~~ name ~~of the author~~ is ~~Jayson~~. I ~~am presently a travel agent. One of the things she loves most is canoeing and she's been performing it for quite a while. For many years he's been residing~~ in ~~Mississippi and he doesn't plan on changing it~~.<br><br>~~Stop by~~ my ~~web blog~~ :: ~~real psychic readings (~~[http://~~www~~.~~chk~~.~~woobi.co.kr~~/~~xe/?document_srl=346069 My Web Page~~])		Мy name is Calvin Aгriaga. I life in Bayonne (Francе).<br><br>my page :: [http://getlivejasmincreditshack.blogspot.com/ LiveJasmin Credits Hack]

en>Chris857: Undid revision 596995675 by 76.231.204.180 (talk) test edit

2014-02-25T00:25:18Z

Undid revision 596995675 by 76.231.204.180 (talk) test edit

← Older revision		Revision as of 02:25, 25 February 2014
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	~~In [[mathematics]], the '''Stein–Strömberg theorem''' or '''Stein–Strömberg inequality''' is a result in [[measure theory]] concerning the [[Hardy–Littlewood maximal operator]].~~ The ~~result is foundational in the study~~ of the ~~problem of [[differentiation of integrals]]. The result~~ is ~~named after the [[mathematician]]s [[Elias M~~. ~~Stein]] and [[Jan-Olov Strömberg]]~~.		The name of the author is Jayson. I am presently a travel agent. One of the things she loves most is canoeing and she's been performing it for quite a while. For many years he's been residing in Mississippi and he doesn't plan on changing it.<br><br>Stop by my web blog :: real psychic readings ([http://www.chk.woobi.co.kr/xe/?document_srl=346069 My Web Page])

	~~==Statement~~ of the ~~theorem==~~
	~~Let ''λ''<sup>''n''</sup> denote ''n''-[[dimension]]al [[Lebesgue measure]] on ''n''-dimensional [[Euclidean space]] '''R'''<sup>''n''</sup>~~ and ~~let~~ '~~'M'' denote the Hardy–Littlewood maximal operator:~~ for a ~~function ''f'' : '''R'''<sup>''n''</sup> → '''R''', ''Mf'' : '''R'''<sup>''n''</sup> → '''R''' is defined by~~

	~~:<math>Mf(x) = \sup_{r > 0} \frac1{\lambda^{n} \big( B_{r} (x) \big)} \int_{B_{r} (x)} \| f(y) \| \, \mathrm{d} \lambda^{n} (y),</math>~~

	~~where ''B''<sub>''r''</sub>(''x'') denotes the [[open ball]] of [[radius]] ''r'' with center ''x''~~. ~~Then, for each ''p'' > 1, there is a constant ''C'~~'~~<sub>''p''</sub> > 0 such that, for all [[natural number]]~~s ~~''n''~~ and ~~functions ''f'' ∈ ''L'~~'<~~sup~~>~~''p''~~<~~/sup~~>~~('''R'''<sup>''n''</sup>; '''R'''),~~

	:~~<math>\\| Mf \\|_{L^{p}} \leq C_{p} \\| f \\|_{L^{p}}.</math>~~

	~~In general, a maximal operator ''M'' is said to be of '''strong type'''~~ (~~''p'', ''p'') if~~

	:~~<math>\\| Mf \\|_{L^{p}} \leq C_{p, n} \\| f \\|_{L^{p}}<~~/~~math>~~

	~~for all ''f'' ∈ ''L''<sup>''p''</sup>('''R'''<sup>''n''<~~/sup>; '''R'''). Thus, the Stein–Strömberg theorem is the statement that the Hardy–Littlewood maximal operator is of strong type (''p'', ''p'') uniformly with respect to the dimension ''n''.

	~~==References==~~
	* {{cite journal
	~~\| last = Stein~~
	~~\| first = Elias M.~~
	~~\| authorlink = Elias M. Stein~~
	~~\| coauthors = Strömberg, Jan-Olov~~
	~~\| title = Behavior of maximal functions in '''R'''<sup>''n''</sup> for large ''n''~~
	~~\| journal = Ark~~. ~~Mat~~.
	~~\| volume = 21~~
	~~\| year = 1983~~
	~~\| issue = 2~~
	~~\| pages = 259–269~~
	~~\| doi = 10~~.~~1007~~/~~BF02384314~~
	~~}} {{MathSciNet\|id=727348}}~~
	* {{cite journal
	~~\| last = Tišer~~
	~~\| first = Jaroslav~~
	~~\| title = Differentiation theorem for Gaussian measures on Hilbert space~~
	~~\| journal = Trans. Amer. Math. Soc.~~
	~~\| volume = 308~~
	~~\| year = 1988~~
	~~\| issue = 2~~
	~~\| pages = 655–666~~
	~~\| doi = 10.2307~~/~~2001096~~
	~~}} {{MathSciNet\|id~~=~~951621}}~~

	~~{{DEFAULTSORT:Stein-Stromberg theorem}}~~
	~~[[Category:Inequalities]]~~
	~~[[Category:Theorems in measure theory]]~~
	~~[[Category:Operator theory]~~]

en>Chris857: Undid revision 593414326 by 118.102.222.188 (talk) test edit

2014-02-02T03:35:21Z

Undid revision 593414326 by 118.102.222.188 (talk) test edit

← Older revision		Revision as of 05:35, 2 February 2014
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	~~Golda~~ is ~~what'~~s ~~created clairvoyants (~~[~~http://findyourflirt~~.~~net/index~~.~~php?m~~=~~member_profile&p~~=~~profile~~&~~id=117823 findyourflirt.net~~]) on ~~my beginning certificate although it~~ is ~~not~~ the ~~name on my beginning certificate~~. ~~Since he was eighteen he~~'s ~~been operating as an information officer but he ideas on altering it~~. ~~What me and my family members love~~ is ~~performing ballet but I~~'~~ve been taking on new issues recently. [http~~://~~help~~.~~ksu~~.~~edu~~.~~sa/node/65129 online psychic reading] Ohio is where her home is~~.<br><br>~~Here is my web-site [http:~~/~~/gcjcteam~~.~~org/index~~.~~php?mid~~=~~etc_video&document_srl~~=~~696611~~&~~sort_index~~=~~regdate&order_type~~=~~desc online psychic readings~~]		In [[mathematics]], the '''Stein–Strömberg theorem''' or '''Stein–Strömberg inequality''' is a result in [[measure theory]] concerning the [[Hardy–Littlewood maximal operator]]. The result is foundational in the study of the problem of [[differentiation of integrals]]. The result is named after the [[mathematician]]s [[Elias M. Stein]] and [[Jan-Olov Strömberg]].

			==Statement of the theorem==
			Let ''λ''<sup>''n''</sup> denote ''n''-[[dimension]]al [[Lebesgue measure]] on ''n''-dimensional [[Euclidean space]] '''R'''<sup>''n''</sup> and let ''M'' denote the Hardy–Littlewood maximal operator: for a function ''f'' : '''R'''<sup>''n''</sup> → '''R''', ''Mf'' : '''R'''<sup>''n''</sup> → '''R''' is defined by

			:<math>Mf(x) = \sup_{r > 0} \frac1{\lambda^{n} \big( B_{r} (x) \big)} \int_{B_{r} (x)} \| f(y) \| \, \mathrm{d} \lambda^{n} (y),</math>

			where ''B''<sub>''r''</sub>(''x'') denotes the [[open ball]] of [[radius]] ''r'' with center ''x''. Then, for each ''p'' > 1, there is a constant ''C''<sub>''p''</sub> > 0 such that, for all [[natural number]]s ''n'' and functions ''f'' ∈ ''L''<sup>''p''</sup>('''R'''<sup>''n''</sup>; '''R'''),

			:<math>\\| Mf \\|_{L^{p}} \leq C_{p} \\| f \\|_{L^{p}}.</math>

			In general, a maximal operator ''M'' is said to be of '''strong type''' (''p'', ''p'') if

			:<math>\\| Mf \\|_{L^{p}} \leq C_{p, n} \\| f \\|_{L^{p}}</math>

			for all ''f'' ∈ ''L''<sup>''p''</sup>('''R'''<sup>''n''</sup>; '''R'''). Thus, the Stein–Strömberg theorem is the statement that the Hardy–Littlewood maximal operator is of strong type (''p'', ''p'') uniformly with respect to the dimension ''n''.

			==References==
			* {{cite journal
			\| last = Stein
			\| first = Elias M.
			\| authorlink = Elias M. Stein
			\| coauthors = Strömberg, Jan-Olov
			\| title = Behavior of maximal functions in '''R'''<sup>''n''</sup> for large ''n''
			\| journal = Ark. Mat.
			\| volume = 21
			\| year = 1983
			\| issue = 2
			\| pages = 259–269
			\| doi = 10.1007/BF02384314
			}} {{MathSciNet\|id=727348}}
			* {{cite journal
			\| last = Tišer
			\| first = Jaroslav
			\| title = Differentiation theorem for Gaussian measures on Hilbert space
			\| journal = Trans. Amer. Math. Soc.
			\| volume = 308
			\| year = 1988
			\| issue = 2
			\| pages = 655–666
			\| doi = 10.2307/2001096
			}} {{MathSciNet\|id=951621}}

			{{DEFAULTSORT:Stein-Stromberg theorem}}
			[[Category:Inequalities]]
			[[Category:Theorems in measure theory]]
			[[Category:Operator theory]]

en>Chris857: Undid revision 485163337 by 203.62.173.4 (talk) no idle chitchat

2012-04-02T14:26:44Z

Undid revision 485163337 by 203.62.173.4 (talk) no idle chitchat

New page

Golda is what's created clairvoyants ([http://findyourflirt.net/index.php?m=member_profile&p=profile&id=117823 findyourflirt.net]) on my beginning certificate although it is not the name on my beginning certificate. Since he was eighteen he's been operating as an information officer but he ideas on altering it. What me and my family members love is performing ballet but I've been taking on new issues recently. [http://help.ksu.edu.sa/node/65129 online psychic reading] Ohio is where her home is.<br><br>Here is my web-site [http://gcjcteam.org/index.php?mid=etc_video&document_srl=696611&sort_index=regdate&order_type=desc online psychic readings]

← Older revision		Revision as of 02:25, 25 February 2014
Line 1:		Line 1:
	~~In [[mathematics]], the '''Stein–Strömberg theorem''' or '''Stein–Strömberg inequality''' is a result in [[measure theory]] concerning the [[Hardy–Littlewood maximal operator]].~~ The ~~result is foundational in the study~~ of the ~~problem of [[differentiation of integrals]]. The result~~ is ~~named after the [[mathematician]]s [[Elias M~~. ~~Stein]] and [[Jan-Olov Strömberg]]~~.		The name of the author is Jayson. I am presently a travel agent. One of the things she loves most is canoeing and she's been performing it for quite a while. For many years he's been residing in Mississippi and he doesn't plan on changing it.<br><br>Stop by my web blog :: real psychic readings ([http://www.chk.woobi.co.kr/xe/?document_srl=346069 My Web Page])

	~~==Statement~~ of the ~~theorem==~~
	~~Let ''λ''<sup>''n''</sup> denote ''n''-[[dimension]]al [[Lebesgue measure]] on ''n''-dimensional [[Euclidean space]] '''R'''<sup>''n''</sup>~~ and ~~let~~ '~~'M'' denote the Hardy–Littlewood maximal operator:~~ for a ~~function ''f'' : '''R'''<sup>''n''</sup> → '''R''', ''Mf'' : '''R'''<sup>''n''</sup> → '''R''' is defined by~~

	~~:<math>Mf(x) = \sup_{r > 0} \frac1{\lambda^{n} \big( B_{r} (x) \big)} \int_{B_{r} (x)} \| f(y) \| \, \mathrm{d} \lambda^{n} (y),</math>~~

	~~where ''B''<sub>''r''</sub>(''x'') denotes the [[open ball]] of [[radius]] ''r'' with center ''x''~~. ~~Then, for each ''p'' > 1, there is a constant ''C'~~'~~<sub>''p''</sub> > 0 such that, for all [[natural number]]~~s ~~''n''~~ and ~~functions ''f'' ∈ ''L'~~'<~~sup~~>~~''p''~~<~~/sup~~>~~('''R'''<sup>''n''</sup>; '''R'''),~~

	:~~<math>\\| Mf \\|_{L^{p}} \leq C_{p} \\| f \\|_{L^{p}}.</math>~~

	~~In general, a maximal operator ''M'' is said to be of '''strong type'''~~ (~~''p'', ''p'') if~~

	:~~<math>\\| Mf \\|_{L^{p}} \leq C_{p, n} \\| f \\|_{L^{p}}<~~/~~math>~~

	~~for all ''f'' ∈ ''L''<sup>''p''</sup>('''R'''<sup>''n''<~~/sup>; '''R'''). Thus, the Stein–Strömberg theorem is the statement that the Hardy–Littlewood maximal operator is of strong type (''p'', ''p'') uniformly with respect to the dimension ''n''.

	~~==References==~~
	* {{cite journal
	~~\| last = Stein~~
	~~\| first = Elias M.~~
	~~\| authorlink = Elias M. Stein~~
	~~\| coauthors = Strömberg, Jan-Olov~~
	~~\| title = Behavior of maximal functions in '''R'''<sup>''n''</sup> for large ''n''~~
	~~\| journal = Ark~~. ~~Mat~~.
	~~\| volume = 21~~
	~~\| year = 1983~~
	~~\| issue = 2~~
	~~\| pages = 259–269~~
	~~\| doi = 10~~.~~1007~~/~~BF02384314~~
	~~}} {{MathSciNet\|id=727348}}~~
	* {{cite journal
	~~\| last = Tišer~~
	~~\| first = Jaroslav~~
	~~\| title = Differentiation theorem for Gaussian measures on Hilbert space~~
	~~\| journal = Trans. Amer. Math. Soc.~~
	~~\| volume = 308~~
	~~\| year = 1988~~
	~~\| issue = 2~~
	~~\| pages = 655–666~~
	~~\| doi = 10.2307~~/~~2001096~~
	~~}} {{MathSciNet\|id~~=~~951621}}~~

	~~{{DEFAULTSORT:Stein-Stromberg theorem}}~~
	~~[[Category:Inequalities]]~~
	~~[[Category:Theorems in measure theory]]~~
	~~[[Category:Operator theory]~~]