I would translate it as “labour jurisdiction”

In most countries (including mine), the courts with jurisdiction to resolve conflicts between workers and their employers are called “labo(u)r courts”, “courts with jurisdiction on labor matters”, and their jurisdiction is called “labo(u)r jurisdiction”. [Tribunales del Trabajo/ jurisdicción laboral]

The term “jurisdicción social” seems to be exclusive to Spain, and the corresponding translation (“corporate jurisdiction”, suggested by Michael Powers) has a completely different meaning in English.

Please see the references below.

Kind regards,

Manuel

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En realidad, nos encontramos con una alteración sustancial de las reglas que han posibilitado la existencia de la Jurisdicción Social como jurisdicción especializada en el conocimiento de las controversias entre empresarios y trabajadores por incidencias derivadas del contrato de trabajo. La especificidad del Ordenamiento Laboral y las adaptaciones procedimentales que imponen las relaciones laborales han venido justificando tanto procedimientos específicos como un Orden Jurisdiccional exclusivo para el conocimiento de estas controversias. El Anteproyecto de Ley Concursal por tanto supone la primera y sustancial reducción del ámbito de competencias del Orden Social, al encomendar al Juez Civil, y más en concreto, al Juez del Concurso, que resuelva los conflictos laborales, aplicando la legislación laboral a empresarios y trabajadores ante cualquier cuestión de índole laboral con tal de que tenga algún tipo de trascendencia patrimonial.

El conjunto de las materias es realmente amplísimo, y de hecho lo que es cuestionable es imaginar que materias se pueden discutir ante un Tribunal que no tengan una repercusión patrimonial más o menos relevante. Ni siquiera se limita el Anteproyecto a reservar las materias que supongan la condena a la empresa a una cantidad de dinero, sino que al referir la regla competencial a las consecuencias patrimoniales de la acción, en realidad está extendiendo su ámbito a prácticamente la totalidad de los procesos laborales en los que se vea inmersa una empresa en situación de crisis concursal.
http://www.madrid.ccoo.es/fse/publicaciones/cuadernos/c2gual...
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Searched the web for "labour jurisdiction"+courts. Results 1 - 10 of about 113. Search took 0.05 seconds.

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Under the Law of 6 December 1985 relating to labour jurisdiction, the formerly separate tribunals respectively competent for white-collar workers ( tribunal arbitral ) and manual workers ( conseil de prud'hommes ) were amalgamated into a single institution called a Tribunal du travail (Labour Tribunal). One such Tribunal exists in each magistrate's area of jurisdiction, and is competent to deal with individual disputes relating to contracts of employment that arise between employers and their employees, including those that occur after the employment has ended.
http://www.eurofound.eu.int/emire/LUXEMBOURG/LABOURJURISDICT...
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Searched the web for "corporate jurisdiction"+courts. Results 1 - 10 of about 129. Search took 0.41 seconds.

Corporate Denial
... have found, what we believe to be that "out" from corporate jurisdiction which has ... of
governors, the president is the corporate CEO, and the "courts" are mere ...
www.detaxcanada.org/corporate.htm - 28k - Cached - Similar pages

Piercing the Corporate Veil
... have found what we believe to be that "out" from corporate jurisdiction (which has ... of
governors, the President is the corporate CEO, and the "courts" are mere ...
www.usa-the-republic.com/abatements/Notary.html - 22k - Cached - Similar pages

MODERN ROBBER BARONS
... Let’s see here what the corporate statutory “rules” say regarding corporate
jurisdiction. ... What this means is that the “courts” (there is no such ...
www.usa-the-republic.com/jurisprudentia/ modern%20robber%20barons.html - 23k - Cached - Similar pages
[ More results from www.usa-the-republic.com ]
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Can we understand what this means? Unless we pierce the corporate veil (legal term) and drag that corporation into the light, redeem ourselves by removing us from that robber baron jurisdiction, we have nor more rights than those corporate entities wish us to have. In short, the constitution is dead for corporate members. Let’s see here what the corporate statutory “rules” say regarding corporate jurisdiction. Article 429 of the Louisiana Criminal Statutes, which may or may not have been rescinded or moved, but makes absolutely no difference, since our constitution, including the Ninth and Tenth Amendments, protects us from this farce, reads:
“On trial of any criminal case it shall not be necessary to prove the incorporation of any corporation mentioned in the indictment, unless the defendant, before entering upon such trial, shall have filed his affidavit specifically denying the existence of such corporation.”
What this means is that the “courts” (there is no such thing as judicial courts any more, as they are all now corporation arbitration boards) take notice of our corporate status (yes, we as individuals are corporations, which the state can and does control) and will treat us accordingly unless we file an affidavit into that “court” before the trial begins, and this treatment is minus the Constitutional safeguards.
http://www.usa-the-republic.com/jurisprudentia/modern robber...
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